Method and apparatus for signal receiving and deinterleaving

ABSTRACT

A signal receiving method include: demodulating a signal received from a transmitting apparatus to generate values based on 1024-quadrature amplitude modulation (QAM); splitting the values into a plurality of groups; deinterleaving the plurality of groups based on a preset interleaving order; and decoding values of the deinterleaved plurality of groups based on a low density parity check (LDPC) code, a code rate of the LDPC code being 6/15 and a code length of the LDPC code being 64800, wherein the plurality of groups are deinterleaved based on a predetermined equation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation of U.S. application Ser. No. 16/925,368 filedJul. 10, 2020, which is a continuation of U.S. application Ser. No.16/352,142 filed Mar. 13, 2019, which is a continuation of U.S.application Ser. No. 15/609,707 filed May 31, 2017 (now U.S. Pat. No.10,270,467), which is a continuation of U.S. application Ser. No.14/662,379 filed Mar. 19, 2015 (now U.S. Pat. No. 9,685,980), whichclaims priority from U.S. Provisional Application No. 61/955,410 filedon Mar. 19, 2014, and Korean Patent Application No. 10-2015-0000677filed on Jan. 5, 2015, the disclosures of which are incorporated hereinby reference in their entirety.

BACKGROUND 1. Field

Apparatuses and methods consistent with exemplary embodiments relate toa transmitting apparatus and an interleaving method thereof, and moreparticularly, to a transmitting apparatus which processes and transmitsdata, and an interleaving method thereof.

2. Description of the Related Art

In the 21st century information-oriented society, broadcastingcommunication services are moving into an era of digitalization,multi-channel, wideband, and high quality. In particular, as higherquality digital televisions, portable multimedia players (PMPs) andportable broadcasting equipment are increasingly used in recent years,there is an increasing demand for methods for supporting variousreceiving methods of digital broadcasting services.

In order to meet such demand, standard groups are establishing variousstandards and are providing a variety of services to satisfy users'needs. Therefore, there is a need for a method for providing improvedservices to users with more robust encoding, decoding and receivingperformance.

SUMMARY

One or more exemplary embodiments may overcome the above disadvantagesand other disadvantages not described above. However, it is understoodthat one or more exemplary embodiment are not required to overcome thedisadvantages described above, and may not overcome any of the problemsdescribed above.

One or more exemplary embodiments provide a transmitting apparatus whichcan map a bit included in a predetermined group from among a pluralityof groups of a Low Density Parity Check (LDPC) codeword onto apredetermined bit of a modulation symbol, and transmit the bit, and aninterleaving method thereof.

According to an aspect of an exemplary embodiment, there is provided atransmitting apparatus which may include: an encoder configured togenerate an LDPC codeword by LDPC encoding based on a parity checkmatrix; an interleaver configured to interleave the LDPC codeword; and amodulator configured to map the interleaved LDPC codeword onto aplurality of modulation symbols, wherein the modulator is configured tomap bits included in a predetermined bit group from among a plurality ofbit groups constituting the LDPC codeword onto a predetermined bit ofeach of the modulation symbols.

Each of the plurality of bit groups may be formed of M number of bits,and M may be a common divisor of N_(ldpc) and K_(ldpc) and determined tosatisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Q_(ldpc) may be a cyclic shiftparameter value regarding columns in a column group of an informationword submatrix of the parity check matrix, N_(ldpc) may be a length ofthe LDPC codeword, and K_(ldpc) may be a length of information word bitsof the LDPC codeword.

The interleaver may include: a parity interleaver configured tointerleave parity bits of the LDPC codeword; a group interleaverconfigured to perform group interleaving on the parity-interleaved LDPCcodeward by dividing the parity-interleaved LDPC codeword by theplurality of bit groups and rearranging an order of the plurality of bitgroups in bits group wise; and a block interleaver configured tointerleave the plurality of bit groups the order of which is rearranged.

The group interleaver may be configured to rearrange the order of theplurality of bit groups in bits group wise by using Equation 15.

In Equation 15, π(j) may be determined based on at least one of a lengthof the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 64800, the modulation method is1024-QAM, and the code rate is 6/15, π(j) may be defined as in table 9.

When the LDPC codeword has a length of 64800, the modulation method is1024-QAM, and the code rate is 8/15, π(j) may be defined as in table 10.

When the LDPC codeword has a length of 64800, the modulation method is1024-QAM, and the code rate is 12/15, π(j) may be defined as in table13:

The block interleaver may be configured to interleave by writing theplurality of bit groups in each of a plurality of columns in bits groupwise in a column direction, and reading each row of the plurality ofcolumns in which the plurality of bit groups are written in bits groupwise in a row direction.

The block interleaver may be configured to serially write, in theplurality of columns, at least one bit group which is writable in theplurality of columns in bits group wise from among the plurality of bitgroups, and divide and write bit groups other than the at least one bitgroup from among the plurality of bit groups in an area of the pluralityof columns other than an area where the at least some bit group iswritten in the plurality of columns in bits group wise.

According to an aspect of another exemplary embodiment, there isprovided an interleaving method of a transmitting apparatus which mayinclude: generating an LDPC codeword by LDPC encoding based on a paritycheck matrix; interleaving the LDPC codeword; and mapping theinterleaved LDPC codeword onto a plurality of modulation symbols,wherein the mapping comprises mapping bits included in a predeterminedbit group from among a plurality of bit groups constituting the LDPCcodeword onto a predetermined bit of each of the modulation symbols.

Each of the plurality of bit groups may be formed of 360 bits, and M maybe a common divisor of N_(ldpc) and K_(ldpc) and may be determined tosatisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Q_(ldpc) may be a cyclic shiftparameter value regarding columns in a column group of an informationword submatrix of the parity check matrix, N_(ldpc) may be a length ofthe LDPC codeword, and K_(ldpc) may be a length of information word bitsof the LDPC codeword.

The interleaving may include: interleaving parity bits of the LDPCcodeword; group interleaving on the parity-interleaved LDPC codeward bydividing the parity-interleaved LDPC codeword by the plurality of bitgroups and rearranging an order of the plurality of bit groups in bitsgroup wise; and; and interleaving the plurality of bit groups the orderof which is rearranged.

The rearranging in bits group wise may include rearranging the order ofthe plurality of bit groups in bits group wise by using Equation 15.

In Equation 15, π(j) may be determined based on at least one of a lengthof the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 64800, the modulation method is1024-QAM, and the code rate is 6/15, π(j) may be defined as in table 9.

When the LDPC codeword has a length of 64800, the modulation method is1024-QAM, and the code rate is 8/15, π(j) may be defined as in table 10.

When the LDPC codeword has a length of 64800, the modulation method is1024-QAM, and the code rate is 12/15, π(j) may be defined as in table13.

The interleaving the plurality of bit groups may include interleaving bywriting the plurality of bit groups in each of a plurality of columns inbits group wise in a column direction, and reading each row of theplurality of columns in which the plurality of bit groups are written inbits group wise in a row direction.

The interleaving the plurality of bit groups may include: seriallywriting, in the plurality of columns, at least one bit group which iswritable in the plurality of columns in bits group wise from among theplurality of bit groups; and dividing and writing bit groups other thanthe at least one bit group from among the plurality of bit groups in anarea of the plurality of columns other than an area where the at leastsome bit group is written in the plurality of columns in bits groupwise.

According to various exemplary embodiments as described above, improveddecoding and receiving performance can be provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects will be more apparent by describing indetail exemplary embodiments, with reference to the accompanyingdrawings, in which:

FIG. 1 is a block diagram to illustrate a configuration of atransmitting apparatus according to an exemplary embodiment;

FIGS. 2 and 3 are views to illustrate a configuration of a parity checkmatrix according to various exemplary embodiments;

FIG. 4 is a block diagram to illustrate a configuration of aninterleaver according to an exemplary embodiment;

FIGS. 5 to 7 are views to illustrate a method for processing an LDPCcodeword on a group basis according to exemplary embodiments;

FIGS. 8 to 12 are views to illustrate a configuration of a blockinterleaver and an interleaving method according to exemplaryembodiments;

FIG. 13 is a view to illustrate an operation of a demultiplexeraccording to an exemplary embodiment;

FIG. 14 is a block diagram to illustrate a configuration of aninterleaver according to another exemplary embodiment;

FIGS. 15-17 are views to illustrate a configuration of a block-rowinterleaver and an interleaving method according to exemplaryembodiments;

FIG. 18 is a block diagram to illustrate a configuration of a receivingapparatus according to an exemplary embodiment;

FIGS. 19 and 21 are block diagrams to illustrate a configuration of adeinterleaver according to exemplary embodiments;

FIG. 20 is a view to illustrate a deinterleaving method of a blockdeinterleaver according to an exemplary embodiment; and

FIG. 22 is a flowchart to illustrate an interleaving method according toan exemplary embodiment.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Hereinafter, various exemplary embodiments will be described in greaterdetail with reference to the accompanying drawings.

In the following description, the same reference numerals are used forthe same elements when they are depicted in different drawings. Thematters defined in the description, such as detailed construction andelements, are provided to assist in a comprehensive understanding of theexemplary embodiments. Thus, it is apparent that the exemplaryembodiments can be carried out without those specifically definedmatters. Also, functions or elements known in the related art are notdescribed in detail since they would obscure the exemplary embodimentswith unnecessary detail.

FIG. 1 is a block diagram to illustrate a configuration of atransmitting apparatus according to an exemplary embodiment. Referringto FIG. 1 , the transmitting apparatus 100 includes an encoder 110, aninterleaver 120, and a modulator 130 (or a constellation mapper).

The encoder 110 generates a Low Density Parity Check (LDPC) codeword byperforming LDPC encoding based on a parity check matrix. The encoder 110may include an LDPC encoder (not shown) to perform the LDPC encoding.

Specifically, the encoder 110 LDPC-encodes information word (orinformation) bits to generate the LDPC codeword which is formed of theinformation word bits and parity bits (that is, LDPC parity bits). Here,bits input to the encoder 110 may be used as the information word bits.Also, since the LDPC code is a systematic code, the information wordbits may be included in the LDPC codeword as they are.

The LDPC codeword is formed of the information word bits and the paritybits. For example, the LDPC codeword is formed of N_(ldpc) number ofbits, and includes K_(ldpc) number of information word bits andN_(parity)=N_(ldpc)−K_(ldpc) number of parity bits.

In this case, the encoder 110 may generate the LDPC codeword byperforming the LDPC encoding based on the parity check matrix. That is,since the LDPC encoding is a process for generating an LDPC codeword tosatisfy H·C^(T)=0, the encoder 110 may use the parity check matrix whenperforming the LDPC encoding. Herein, H is a parity check matrix and Cis an LDPC codeword.

For the LDPC encoding, the transmitting apparatus 100 may include aseparate memory and may pre-store parity check matrices of variousformats.

For example, the transmitting apparatus 100 may pre-store parity checkmatrices which are defined in Digital Video Broadcasting-Cable version 2(DVB-C2), Digital Video Broadcasting-Satellite-Second Generation(DVB-S2), Digital Video Broadcasting-Second Generation Terrestrial(DVB-T2), etc., or may pre-store parity check matrices which are definedin the North America digital broadcasting standard system AdvancedTelevision System Committee (ATSC) 3.0 standards, which are currentlybeing established. However, this is merely an example and thetransmitting apparatus 100 may pre-store parity check matrices of otherformats in addition to these parity check matrices.

Hereinafter, a parity check matrix according to various exemplaryembodiments will be explained in detail with reference to the drawings.In the parity check matrix, elements other than elements with 1 have 0.

For example, the parity check matrix according to an exemplaryembodiment may have the configuration of FIGS. 2 and 3 .

Referring to FIG. 2 , the parity check matrix 200 is formed of aninformation word submatrix (or information submatrix) 210 correspondingto information word bits, and a parity submatrix 220 corresponding toparity bits. In the parity check matrix 200, elements other thanelements with 1 have 0.

The information word submatrix 210 includes K_(ldpc) number of columnsand the parity submatrix 220 includes N_(parity)=N_(ldpc)−K_(ldpc)number of columns. The number of rows of the parity check matrix 200 isidentical to the number of columns of the parity submatrix 220,N_(parity)=N_(ldpc)−K_(ldpc).

In addition, in the parity check matrix 200, N_(ldpc) is a length of anLDPC codeword, K_(ldpc) is a length of information word bits, andN_(parity)=N_(ldpc)−K_(ldpc) is a length of parity bits. The length ofthe LDPC codeword, the information word bits, and the parity bits meanthe number of bits included in each of the LDPC codeword, theinformation word bits, and the parity bits.

Hereinafter, the configuration of the information word submatrix 210 andthe parity submatrix 220 will be explained in detail.

The information word submatrix 210 includes K_(ldpc) number of columns(that is, 0^(th) column to (K_(ldpc)−1)^(th) column), and follows thefollowing rules:

First, M number of columns from among K_(ldpc) number of columns of theinformation word submatrix 210 belong to a same group, and K_(ldpc)number of columns is divided into K_(ldpc)/M number of column groups. Ineach column group, a column is cyclic-shifted from an immediatelyprevious column by Q_(ldpc) or Q_(ldpc) number of bits. That is,Q_(ldpc) may be a cyclic shift parameter value regarding columns in acolumn group of the information word submatrix 210 of the parity checkmatrix 200.

Herein, M is an interval at which a pattern of a column group, whichincludes a plurality of columns, is repeated in the information wordsubmatrix 210 (e.g., M=360), and Q_(ldpc) is a size by which one columnis cyclic-shifted from an immediately previous column in a same columngroup in the information word submatrix 210. Also, M is a common divisorof N_(ldpc) and K_(ldpc) and is determined to satisfyQ_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Here, M and Q_(ldpc) are integers andK_(ldpc)/M is also an integer. M and Q_(ldpc) may have various valuesaccording to the length of the LDPC codeword and a code rate (CR) or acoding rate.

For example, when M=360 and the length of the LDPC codeword, N_(ldpc),is 64800, Q_(ldpc) may be defined as in Table 1 presented below, and,when M=360 and the length N_(ldpc) of the LDPC codeword is 16200,Q_(ldpc) may be defined as in Table 2 presented below.

TABLE 1 Code Rate N_(ldpc) M Q_(ldpc) 5/15 64800 360 120 6/15 64800 360108 7/15 64800 360 96 8/15 64800 360 84 9/15 64800 360 72 10/15  64800360 60 11/15  64800 360 48 12/15  64800 360 36 13/15  64800 360 24

TABLE 2 Code Rate N_(ldpc) M Q_(ldpc) 5/15 16200 360 30 6/15 16200 36027 7/15 16200 360 24 8/15 16200 360 21 9/15 16200 360 18 10/15  16200360 15 11/15  16200 360 12 12/15  16200 360 9 13/15  16200 360 6

Second, when the degree of the 0^(th) column of the i^(th) column group(i=0, 1, . . . , K_(ldpc)/M−1) is D_(i) (herein, the degree is thenumber of value 1 existing in each column and all columns belonging tothe same column group have the same degree), and a position (or anindex) of each row where 1 exists in the 0^(th) column of the i^(th)column group is R_(i,0) ⁽⁰⁾; R_(i,0) ⁽¹⁾, . . . , R_(i,0) ^((D) ^(i)⁻¹⁾, an index R_(i,j) ^((k)) of a row where k^(th) 1 is located in thej^(th) column in the i^(th) column group is determined by followingEquation 1:R _(i,j) ^((k)) =R _(i,(j−1)) ^((k))Q_(ldpc) mod(N _(ldpc) −K_(ldpc))  (1),where k=0, 1, 2, . . . D_(i)−1; i=0, 1, . . . , K_(ldpc)/M−1; and j=1,2, . . . , M−1.

Equation 1 can be expressed as following Equation 2:R _(i,j) ^((k)) ={R _(i,0) ^((k))+(j mod M)×Q _(ldpc)} mod(N _(ldpc) −K_(ldpc))  (2),where k=0, 1, 2, . . . D_(i)−1; i=0, 1, . . . , K_(ldpc)/M−1; and j=1,2, . . . , M−1. Since j=1, 2, . . . , M−1, (j mod M) of Equation 2 maybe regarded as j.

In the above equations, R_(i,j) ^((k)) is an index of a row where k^(th)1 is located in the j^(th) column in the i^(th) column group, N_(ldpc)is a length of an LDPC codeword, K_(ldpc) is a length of informationword bits, D_(i) is a degree of columns belonging to the i^(th) columngroup, M is the number of columns belonging to a single column group,and Q_(ldpc) is a size by which each column in the column group iscyclic-shifted.

As a result, referring to these equations, when only R_(i,0) ^((k)) isknown, the index R_(i,j) ^((k)) of the row where the k^(th) 1 is locatedin the j^(th) column in the i^(th) column group can be known. Therefore,when the index value of the row where the k^(th) 1 is located in the0^(th) column of each column group is stored, a position of column androw where 1 is located in the parity check matrix 200 having theconfiguration of FIG. 2 (that is, in the information word submatrix 210of the parity check matrix 200) can be known.

According to the above-described rules, all of the columns belonging tothe i^(th) column group have the same degree D_(i). Accordingly, theLDPC codeword which stores information on the parity check matrixaccording to the above-described rules may be briefly expressed asfollows.

For example, when N_(ldpc) is 30, K_(ldpc) is 15, and Q_(ldpc) is 3,position information of the row where 1 is located in the 0^(th) columnof the three column groups may be expressed by a sequence of Equations 3and may be referred to as “weight-1 position sequence”.R _(1,0) ⁽¹⁾=1,R _(1,0) ⁽²⁾=2,R _(1,0) ⁽³⁾=8,R _(1,0) ⁽⁴⁾=10,R _(2,0) ⁽¹⁾=0,R _(2,0) ⁽²⁾=9,R _(2,0) ⁽³⁾=13,R _(3,0) ⁽¹⁾=0,R _(3,0) ⁽²⁾=14.  (3),where R_(i,j) ^((k)) is an index of a row where k^(th) 1 is located inthe j^(th) column in the i^(th) column group.

The weight-1 position sequence like Equation 3 which expresses an indexof a row where 1 is located in the 0^(th) column of each column groupmay be briefly expressed as in Table 3 presented below:

TABLE 3 1 2 8 10 0 9 13 0 14

Table 3 shows positions of elements having value 1 in the parity checkmatrix, and the i^(th) weight-1 position sequence is expressed byindexes of rows where 1 is located in the 0^(th) column belonging to thei^(th) column group.

The information word submatrix 210 of the parity check matrix accordingto an exemplary embodiment may be defined as in Tables 4 to 8 presentedbelow, based on the above descriptions.

Specifically, Tables 4 to 8 show indexes of rows where 1 is located inthe 0th column of the i^(th) column group of the information wordsubmatrix 210. That is, the information word submatrix 210 is formed ofa plurality of column groups each including M number of columns, andpositions of 1 in the 0^(th) column of each of the plurality of columngroups may be defined by Tables 4 to 8.

Herein, the indexes of the rows where 1 is located in the 0^(th) columnof the i^(th) column group mean “addresses of parity bit accumulators”.The “addresses of parity bit accumulators” have the same meaning asdefined in the DVB-C2/S2/T2 standards or the ATSC 3.0 standards whichare currently being established, and thus, a detailed explanationthereof is omitted.

For example, when the length N_(ldpc) of the LDPC codeword is 64800, thecode rate is 6/15, and M is 360, the indexes of the rows where 1 islocated in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are as shown in Table 4 presented below:

TABLE 4 0 1606 3402 4961 6751 7132 11516 12300 12482 12592 13342 1376414123 21576 23946 24533 25376 25667 26836 31799 34173 35462 36153 3674037085 37152 37468 37658 1 4621 5007 6910 8732 9757 11508 13099 1551316335 18052 19512 21319 23663 25628 27208 31333 32219 33003 33239 3344736200 36473 36938 37201 37283 37495 38642 2 16 1094 2020 3080 4194 50985631 6877 7889 8237 9804 10067 11017 11366 13136 13354 15379 18934 2019924522 26172 28666 30386 32714 36390 37015 37162 3 700 897 1708 6017 64907372 7825 9546 10398 16605 18561 18745 21625 22137 23693 24340 2496625015 26995 28586 28895 29687 33938 34520 34858 37056 38297 4 159 20102573 3617 4452 4958 5556 5832 6481 8227 9924 10836 14954 15594 1662318065 19249 22394 22677 23408 23731 24076 24776 27007 28222 30343 383715 3118 3545 4768 4992 5227 6732 8170 9397 10522 11508 15536 20218 2192128599 29445 29758 29968 31014 32027 33685 34378 35867 36323 36728 3687038335 38623 6 1264 4254 6936 9165 9486 9950 10861 11653 13697 1396115164 15665 18444 19470 20313 21189 24371 26431 26999 28086 28251 2926131981 34015 35850 36129 37186 7 111 1307 1628 2041 2524 5358 7988 819110322 11905 12919 14127 15515 15711 17061 19024 21195 22902 23727 2440124608 25111 25228 27338 35398 37794 38196 8 961 3035 7174 7948 1335513607 14971 18189 18339 18665 18875 19142 20615 21136 21309 21758 2336624745 25849 25962 27583 30006 31118 32106 36469 36583 37920 9 2990 35494273 4808 5707 6021 6509 7456 8240 10044 12262 12660 13085 14750 1568016049 21587 23997 25803 28343 28693 34393 34860 35490 36021 37737 3829610 955 4323 5145 6885 8123 9730 11840 12216 19194 20313 23056 2424824830 25268 26617 26801 28557 29753 30745 31450 31973 32839 33025 3329635710 37366 37509 11 264 605 4181 4483 5156 7238 8863 10939 11251 1296416254 17511 20017 22395 22818 23261 23422 24064 26329 27723 28186 3043431956 33971 34372 36764 38123 12 520 2562 2794 3528 3860 4402 5676 69638655 9018 9783 11933 16336 17193 17320 19035 20606 23579 23769 2412324966 27866 32457 34011 34499 36620 37526 13 10106 10637 10906 34242 141856 15100 19378 21848 15 943 11191 27806 29411 16 4575 6359 13629 1938317 4476 4953 18782 24313 18 5441 6381 21840 35943 19 9638 9763 1254630120 20 9587 10626 11047 25700 21 4088 15298 28768 35047 22 2332 63638782 28863 23 4625 4933 28298 30289 24 3541 4918 18257 31746 25 122125233 26757 34892 26 8150 16677 27934 30021 27 8500 25016 33043 38070 287374 10207 16189 35811 29 611 18480 20064 38261 30 25416 27352 3608938469 31 1667 17614 25839 32776 32 4118 12481 21912 37945 33 5573 1322223619 31271 34 18271 26251 27182 30587 35 14690 26430 26799 34355 3613688 16040 20716 34558 37 2740 14957 23436 32540 38 3491 14365 1468136858 39 4796 6238 25203 27854 40 1731 12816 17344 26025 41 19182 2166223742 27872 42 6502 13641 17509 34713 43 12246 12372 16746 27452 44 158921528 30621 34003 45 12328 20515 30651 31432 46 3415 22656 23427 3639547 632 5209 25958 31085 48 619 3690 19648 37778 49 9528 13581 2696536447 50 2147 26249 26968 28776 51 15698 18209 30683 52 1132 19888 3411153 4608 25513 38874 54 475 1729 34100 55 7348 32277 38587 56 182 1647333082 57 3865 9678 21265 58 4447 20151 27618 59 6335 14371 38711 60 7049695 28858 61 4856 9757 30546 62 1993 19361 30732 63 756 28000 29138 643821 24076 31813 65 4611 12326 32291 66 7628 21515 34995 67 1246 1329430068 68 6466 33233 35865 69 14484 23274 38150 70 21269 36411 37450 7123129 26195 37653

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 8/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 5 presentedbelow:

TABLE 5 i Index of row where 1 is located in the 0th column of the ithcolumn group 0 2768 3039 4059 5856 6245 7013 8157 9341 9802 10470 1152112083 16610 18361 20321 24601 27420 28206 29788 1 2739 8244 8891 915712624 12973 15534 16622 16919 18402 18780 19854 20220 20543 22306 2554027478 27678 28053 2 1727 2268 6246 7815 9010 9556 10134 10472 1138914599 15719 16204 17342 17666 18850 22058 25579 25860 29207 3 28 13463721 5565 7019 9240 12355 13109 14800 16040 16839 17369 17631 1935719473 19891 20381 23911 29683 4 869 2450 4386 5316 6160 7107 10362 1113211271 13149 16397 16532 17113 19894 22043 22784 27383 28615 28804 5 5084292 5831 8559 10044 10412 11283 14810 15888 17243 17538 19903 2052822090 22652 27235 27384 28208 28485 6 389 2248 5840 6043 7000 9054 1107511760 12217 12565 13587 15403 19422 19528 21493 25142 27777 28566 287027 1015 2002 5764 6777 9346 9629 11039 11153 12690 13068 13990 1684117702 20021 24106 26300 29332 30081 30196 8 1480 3084 3467 4401 47985187 7851 11368 12323 14325 14546 16360 17158 18010 21333 25612 2655626906 27005 9 6925 8876 12392 14529 15253 15437 19226 19950 20321 2302123651 24393 24653 26668 27205 28269 28529 29041 29292 10 2547 3404 35384666 5126 5468 7695 8799 14732 15072 15881 17410 18971 19609 19717 2215024941 27908 29018 11 888 1581 2311 5511 7218 9107 10454 12252 1366215714 15894 17025 18671 24304 25316 25556 28489 28977 29212 12 1047 14941718 4645 5030 6811 7868 8146 10611 15767 17682 18391 22614 23021 2376325478 26491 29088 29757 13 59 1781 1900 3814 4121 8044 8906 9175 1115614841 15789 16033 16755 17292 18550 19310 22505 29567 29850 14 1952 30574399 9476 10171 10769 11335 11569 15002 19501 20621 22642 23452 2436025109 25290 25828 28505 29122 15 2895 3070 3437 4764 4905 6670 924411845 13352 13573 13975 14600 15871 17996 19672 20079 20579 25327 2795816 612 1528 2004 4244 4599 4926 5843 7684 10122 10443 12267 14368 1841319058 22985 24257 26202 26596 27899 17 1361 2195 4146 6708 7158 75389138 9998 14862 15359 16076 18925 21401 21573 22503 24146 24247 2777829312 18 5229 6235 7134 7655 9139 13527 15408 16058 16705 18320 1990920901 22238 22437 23654 25131 27550 28247 29903 19 697 2035 4887 52756909 9166 11805 15338 16381 18403 20425 20688 21547 24590 25171 2672628348 29224 29412 20 5379 17329 22659 23062 21 11814 14759 22329 2293622 2423 2811 10296 12727 23 8460 15260 16769 17290 24 14191 14608 2953630187 25 7103 10069 20111 22850 26 4285 15413 26448 29069 27 548 21379189 10928 28 4581 7077 23382 23949 29 3942 17248 19486 27922 30 866810230 16922 26678 31 6158 9980 13788 28198 32 12422 16076 24206 29887 338778 10649 18747 22111 34 21029 22677 27150 28980 35 7918 15423 2767227803 36 5927 18086 23525 37 3397 15058 30224 38 24016 25880 26268 391096 4775 7912 40 3259 17301 20802 41 129 8396 15132 42 17825 2811928676 43 2343 8382 28840 44 3907 18374 20939 45 1132 1290 8786 46 14814710 28846 47 2185 3705 26834 48 5496 15681 21854 49 12697 13407 2217850 12788 21227 22894 51 629 2854 6232 52 2289 18227 27458 53 7593 2193523001 54 3836 7081 12282 55 7925 18440 23135 56 497 6342 9717 57 1119922046 30067 58 12572 28045 28990 59 1240 2023 10933 60 19566 20629 2518661 6442 13303 28813 62 4765 10572 16180 63 552 19301 24286 64 6782 1848021383 65 11267 12288 15758 66 771 5652 15531 67 16131 20047 25649 6813227 23035 24450 69 4839 13467 27488 70 2852 4677 22993 71 2504 2811629524 72 12518 17374 24267 73 1222 11859 27922 74 9660 17286 18261 75232 11296 29978 76 9750 11165 16295 77 4894 9505 23622 78 10861 1198014110 79 2128 15883 22836 80 6274 17243 21989 81 10866 13202 22517 8211159 16111 21608 83 3719 18787 22100 84 1756 2020 23901 85 20913 2947330103 86 2729 15091 26976 87 4410 8217 12963 88 5395 24564 28235 89 385917909 23051 90 5733 26005 29797 91 1935 3492 29773 92 11903 21380 2991493 6091 10469 29997 94 2895 8930 15594 95 1827 10028 20070

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 10/15, and M is 360, the indexes of rows where 1exists in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are defined as shown in Table 6 or 7below.

TABLE 6 i Index of row where 1 is located in the 0th column of the ithcolumn group 0 979 1423 4166 4609 6341 8258 10334 10548 14098 1451417051 17333 17653 17830 17990 1 2559 4025 6344 6510 9167 9728 1131214856 17104 17721 18600 18791 19079 19697 19840 2 3243 6894 7950 1053912042 13233 13938 14752 16449 16727 17025 18297 18796 19400 21577 3 32723574 6341 6722 9191 10807 10957 12531 14036 15580 16651 17007 1730919415 19845 4 155 4598 10201 10975 11086 11296 12713 15364 15978 1639517542 18164 18451 18612 20617 5 1128 1999 3926 4069 5558 6085 6337 838610693 12450 15438 16223 16370 17308 18634 6 2408 2929 3630 4357 58527329 8536 8695 10603 11003 14304 14937 15767 18402 21502 7 199 3066 64466849 8973 9536 10452 12857 13675 15913 16717 17654 19802 20115 21579 8312 870 2095 2586 5517 6196 6757 7311 7368 13046 15384 18576 20349 2142421587 9 985 1591 3248 359 3706 3847 6174 6276 7864 9033 13618 1567516446 18355 18843 10 979 3774 4083 5825 6166 7218 7633 9657 10103 1305214240 17320 18126 19544 20208 11 1795 2005 2544 3418 6148 8051 9066 972510676 10752 11512 15171 17523 20481 21059 12 167 315 1824 2325 2640 28686070 6597 7016 8109 9815 11608 16142 17912 19625 13 1298 1896 3039 43034690 8787 12241 13600 14478 15492 16602 17115 17913 19466 20597 14 5683695 6045 6624 8131 8404 8590 9059 9246 11570 14336 18657 18941 1921821506 15 228 1889 1967 2299 3011 5074 7044 7596 7689 9534 10244 1069711691 17902 21410 16 1330 1579 1739 2234 3701 3865 5713 6677 7263 1117212143 12765 17121 20011 21436 17 303 1668 2501 4925 5778 5985 9635 1014010820 11779 11849 12058 15650 20426 20527 18 698 2484 3071 3219 40544125 5663 5939 6928 7086 8054 12173 16280 17945 19302 19 232 1619 30404901 7438 8135 9117 9233 10131 13321 17347 17436 18193 18586 19929 20 123721 6254 6609 7880 8139 10437 12262 13928 14065 14149 15032 15694 1626418883 21 482 915 1548 1637 6687 9338 10163 11768 11970 15524 15695 1738618787 19210 19340 22 1291 2500 4109 4511 5099 5194 10014 13165 1325613972 15409 16113 16214 18584 20998 23 1761 4778 7444 7740 8129 83418931 9136 9207 10003 10678 13959 17673 18194 20990 24 3060 3522 53615692 6833 8342 8792 11023 11211 11548 11914 13987 15442 15541 19707 251322 2348 2970 5632 6349 7577 8782 9113 9267 9376 12042 12943 1668016970 21321 26 6785 11960 21455 27 1223 15672 19550 28 5976 11335 2038529 2818 9387 15317 30 2763 3554 18102 31 5230 11489 18997 32 5809 1577920674 33 2620 17838 18533 34 3025 9342 9931 35 3728 5337 12142 36 25206666 9164 37 12892 15307 20912 38 10736 12393 16539 39 1075 2407 1285340 4921 5411 18206 41 5955 15647 16838 42 6384 10336 19266 43 429 1042117266 44 4880 10431 12208 45 2910 11895 12442 46 7366 18362 18772 474341 7903 14994 48 4564 6714 7378 49 4639 8652 18871 50 15787 1804820246 51 3241 11079 13640 52 1559 2936 15881 53 2737 6349 10881 54 1039416107 17073 55 8207 9043 12874 56 7805 16058 17905 57 11189 15767 1776458 5823 12923 14316 59 11080 20390 20924 60 568 8263 17411 61 1845 35576562 62 2890 10936 14756 63 9031 14220 21517 64 3529 12955 15902 65 4136750 8735 66 6784 12092 16421 67 12019 13794 15308 68 12588 15378 1767669 8067 14589 19304 70 1244 5877 6085 71 15897 19349 19993 72 1426 239412264 73 3456 8931 12075 74 13342 15273 20351 75 9138 13352 20798 767031 7626 14081 77 4280 4507 15617 78 4170 10569 14335 79 3839 751416578 80 4688 12815 18782 81 4861 7858 9435 82 605 5445 12912 83 22804734 7311 84 6668 8128 12638 85 3733 10621 19534 86 13933 18316 19341 871786 3037 21566 88 2202 13239 16432 89 4882 5808 9300 90 4580 8484 1675491 14630 17502 18269 92 6889 11119 12447 93 8162 9078 16330 94 653817851 18100 95 17763 19793 20816 96 2183 11907 17567 97 6640 14428 1517598 877 12035 14081 99 1336 6468 12328 100 5948 9146 12003 101 3782 569912445 102 1770 7946 8244 103 7384 12639 14989 104 1469 11586 20959 1057943 10450 15907 106 5005 8153 10035 107 17750 18826 21513 108 4725 804110112 109 3837 16266 17376 110 11340 17361 17512 111 1269 4611 4774 1122322 10813 16157 113 16752 16843 18959 114 70 4325 18753 115 3165 815315384 116 160 8045 16823 117 14112 16724 16792 118 4291 7667 18176 1195943 19879 20721

TABLE 7 i Index of row where 1 is located in the 0th column of the ithcolumn group 0 316 1271 3692 9495 12147 12849 14928 16671 16938 1786419108 20502 21097 21115 1 2341 2559 2643 2816 2865 5137 5331 7000 75238023 10439 10797 13208 15041 2 5556 6858 7677 10162 10207 11349 1232112398 14787 15743 15859 15952 19313 20879 3 349 573 910 2702 3654 62149246 9353 10638 11772 14447 14953 16620 19888 4 204 1390 2887 3835 62306533 7443 7876 9299 10291 10896 13960 18287 20086 5 541 2429 2838 71448523 8637 10490 10585 11074 12074 15762 16812 17900 18548 6 733 16593838 5323 5805 7882 9429 10682 13697 16909 18846 19587 19592 20904 71134 2136 4631 4653 4718 5197 10410 11666 14996 15305 16048 17417 1896020303 8 734 1001 1283 4959 10016 10176 10973 11579 12051 15550 1591519022 19430 20121 9 745 4057 5855 9885 10594 10989 13156 13219 1335113631 13685 14577 17713 20386 10 968 1446 2130 2502 3092 3787 5323 81048418 9998 11681 13972 17747 17929 11 3020 3857 5275 5786 6319 8608 1194314062 17144 17752 18001 18453 19311 21414 12 709 747 1038 2181 5320 829210584 10859 13964 15009 15277 16953 20675 21509 13 1663 3247 5003 57607186 7360 10346 14211 14717 14792 15155 16128 17355 17970 14 516 5781914 6147 9419 11148 11434 13289 13325 13332 19106 19257 20962 21556 155009 5632 6531 9430 9886 10621 11765 13969 16178 16413 18110 18249 2061620759 16 457 2686 3318 4608 5620 5858 6480 7430 9602 12691 14664 1877720152 20848 17 33 2877 5334 6851 7907 8654 10688 15401 16123 17942 1796918747 18931 20224 18 87 897 7636 8663 11425 12288 12672 14199 1643517615 17950 18953 19667 20281 19 1042 1832 2545 2719 2947 3672 3700 62496398 6833 11114 14283 17694 20477 20 326 488 2662 2880 3009 5357 65878882 11604 14374 18781 19051 19057 20508 21 854 1294 2436 2852 4903 64667761 9072 9564 10321 13638 15658 16946 19119 22 194 899 1711 2408 27865391 7108 8079 8716 11453 17303 19484 20989 21389 23 1631 3121 3994 50057810 8850 10315 10589 13407 17162 18624 18758 19311 20301 24 736 24244792 5600 6370 10061 16053 16775 18600 25 1254 8163 8876 9157 1214114587 16545 17175 18191 26 388 6641 8974 10607 10716 14477 16825 1719118400 27 5578 6082 6824 7360 7745 8655 11402 11665 12428 28 3603 872913463 14698 15210 19112 19550 20727 21052 29 48 1732 3805 5158 1544216909 19854 21071 21579 30 11707 14014 21531 31 1542 4133 4925 32 1008313505 21198 33 14300 15765 16752 34 778 1237 11215 35 1325 3199 14534 362007 14510 20599 37 1996 5881 16429 38 5111 15018 15980 39 4989 1068112810 40 3763 10715 16515 41 2259 10080 15642 42 9032 11319 21305 433915 15213 20884 44 11150 15022 20201 45 1147 6749 19625 46 12139 1293918870 47 3840 4634 10244 48 1018 10231 17720 49 2708 13056 13393 50 578111588 18888 51 1345 2036 5252 52 5908 8143 15141 53 1804 13693 18640 5410433 13965 16950 55 9568 10122 15945 56 547 6722 14015 57 321 1284414095 58 2632 10513 14936 59 6369 11995 20321 60 9920 19136 21529 611990 2726 10183 62 5763 12118 15467 63 503 10006 19564 64 9839 1194219472 65 11205 13552 15389 66 8841 13797 19697 67 124 6053 18224 68 647714406 21146 69 1224 8027 16011 70 3046 4422 17717 71 739 12308 17760 724014 4130 7835 73 2266 5652 11981 74 2711 7970 18317 75 2196 15229 1721776 8636 13302 16764 77 5612 15010 16657 78 615 1249 4639 79 3821 1207318506 80 1066 16522 21536 81 11307 18363 19740 82 3240 8560 10391 833124 11424 20779 84 1604 8861 17394 85 2083 7400 8093 86 3218 7454 915587 9855 15998 20533 88 316 2850 20652 89 5583 9768 10333 90 7147 771318339 91 12607 17428 21418 92 14216 16954 18164 93 8477 15970 18488 941632 8032 9751 95 4573 9080 13507 96 11747 12441 13876 97 1183 1560516675 98 4408 10264 17109 99 5495 7882 12150 100 1010 3763 5065 101 982818054 21599 102 6342 7353 15358 103 6362 9462 19999 104 7184 13693 17622105 4343 4654 10995 106 7099 8466 18520 107 11505 14395 15138 108 677916691 18726 109 7146 12644 20196 110 5865 16728 19634 111 4657 871421246 112 4580 5279 18750 113 3767 6620 18905 114 9209 13093 17575 11512486 15875 19791 116 8046 14636 17491 117 2120 4643 13206 118 6186 967512601 119 784 5770 21585

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 12/15, and M is 360, the indexes of rows where 1exists in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are defined as shown in Table 8 below.

TABLE 8 i Index of row where 1 is located in the 0th column of the ithcolumn group 0 584 1472 1621 1867 3338 3568 3723 4185 5126 5889 77378632 8940 9725 1 221 445 590 3779 3835 6939 7743 8280 8448 8491 936710042 11242 12917 2 4662 4837 4900 5029 6449 6687 6751 8684 9936 1168111811 11886 12089 12909 3 2418 3018 3647 4210 4473 7447 7502 9490 1006711092 11139 11256 12201 12383 4 2591 2947 3349 3406 4417 4519 5176 66728498 8863 9201 11294 11376 12184 5 27 101 197 290 871 1727 3911 54116676 8701 9350 10310 10798 12439 6 1765 1897 2923 3584 3901 4048 69637054 7132 9165 10184 10824 11278 12669 7 2183 3740 4808 5217 5660 63756787 8219 8466 9037 10353 10583 11118 12762 8 73 1594 2146 2715 35013572 3639 3725 6959 7187 8406 10120 10507 10691 9 240 732 1215 2185 27882830 3499 3881 4197 4991 6425 7061 9756 10491 10 831 1568 1828 3424 43194516 4639 6018 9702 10203 10417 11240 11518 12458 11 2024 2970 3048 36383676 4152 5284 5779 5926 9426 9945 10873 11787 11837 12 1049 1218 16512328 3493 4363 5750 6483 7613 8782 9738 9803 11744 11937 13 1193 20602289 2964 3478 4592 4756 6709 7162 8231 8326 11140 11908 12243 14 9782120 2439 3338 3850 4589 6567 8745 9656 9708 10161 10542 10711 12639 152403 2938 3117 3247 3711 5593 5844 5932 7801 10152 10226 11498 1216212941 16 1781 2229 2276 2533 3582 3951 5279 5774 7930 9824 10920 1103812340 12440 17 289 384 1980 2230 3464 3873 5958 8656 8942 9006 1017511425 11745 12530 18 155 354 1090 1330 2002 2236 3559 3705 4922 59586576 8564 9972 12760 19 303 876 2059 2142 5244 5330 6644 7576 8614 959810410 10718 11033 12957 20 3449 3617 4408 4602 4727 6182 8835 8928 93729644 10237 10747 11655 12747 21 811 2565 2820 8677 8974 9632 11069 1154811839 12107 12411 12695 12812 12890 22 972 4123 4943 6385 6449 7339 74778379 9177 9359 10074 11709 12552 12831 23 842 973 1541 2262 2905 52766758 7099 7894 8128 8325 8663 8875 10050 24 474 791 968 3902 4924 49655085 5908 6109 6329 7931 9038 9401 10568 25 1397 4461 4658 5911 60377127 7318 8678 8924 9000 9473 9602 10446 12692 26 1334 7571 12881 271393 1447 7972 28 633 1257 10597 29 4843 5102 11056 30 3294 8015 1051331 1108 10374 10546 32 5353 7824 10111 33 3398 7674 8569 34 7719 947810503 35 2997 9418 9581 36 5777 6519 11229 37 1966 5214 9899 38 6 40885827 39 836 9248 9612 40 483 7229 7548 41 7865 8289 9804 42 2915 1109811900 43 6180 7096 9481 44 1431 6786 8924 45 748 6757 8625 46 3312 44757204 47 1852 8958 11020 48 1915 2903 4006 49 6776 10886 12531 50 25949998 12742 51 159 2002 12079 52 853 3281 3762 53 5201 5798 6413 54 38826062 12047 55 4133 6775 9657 56 228 6874 11183 57 7433 10728 10864 587735 8073 12734 59 2844 4621 11779 60 3909 7103 12804 61 6002 9704 1106062 5864 6856 7681 63 3652 5869 7605 64 2546 2657 4461 65 2423 4203 911166 244 1855 4691 67 1106 2178 6371 68 391 1617 10126 69 250 9259 1060370 3435 4614 6924 71 1742 8045 9529 72 7667 8875 11451 73 4023 6108 691174 8621 10184 11650 75 6726 10861 12348 76 3228 6302 7388 77 1 1137 535878 381 2424 8537 79 3256 7508 10044 80 1980 2219 4569 81 2468 5699 1031982 2803 3314 12808 83 8578 9642 11533 84 829 4585 7923 85 59 329 5575 861067 5709 6867 87 1175 4744 12219 88 109 2518 6756 89 2105 10626 1115390 5192 10696 10749 91 6260 7641 8233 92 2998 3094 11214 93 3398 646611494 94 6574 10448 12160 95 2734 10755 12780 96 1028 7958 10825 97 85458602 10793 98 392 3398 11417 99 6639 9291 12571 100 1067 7919 8934 1011064 2848 12753 102 6076 8656 12690 103 5504 6193 10171 104 1951 71567356 105 4389 4780 7889 106 526 4804 9141 107 1238 3648 10464 108 25875624 12557 109 5560 5903 11963 110 1134 2570 3297 111 10041 11583 12157112 1263 9585 12912 113 3744 7898 10646 114 45 9074 10315 115 1051 618810038 116 2242 8394 12712 117 3598 9025 12651 118 2295 3540 5610 1191914 4378 12423 120 1766 3635 12759 121 5177 9586 11143 122 943 359011649 123 4864 6905 10454 124 5852 6042 10421 125 6095 8285 12349 1262070 7171 8563 127 718 12234 12716 128 512 10667 11353 129 3629 64857040 130 2880 8865 11466 131 4490 10220 11796 132 5440 8819 9103 1335262 7543 12411 134 516 7779 10940 135 2515 5843 9202 136 4684 599410586 137 573 2270 3324 138 7870 8317 10322 139 6856 7638 12909 140 15837669 10781 141 8141 9085 12555 142 3903 5485 9992 143 4467 11998 12904

In the above-described examples, the length of the LDPC codeword is64800 and the code rate is 6/15, 8/15, 10/15, and 12/15. However, thisis merely an example and the position of 1 in the information wordsubmatrix 210 may be defined variously when the length of the LDPCcodeword is 16200 or the code rate has different values.

According to an exemplary embodiment, even when an order of numbers,i.e., indexes, in a sequence corresponding to the i^(th) column group ofthe parity check matrix 200 as shown in the above-described Tables 4 to8 is changed, the changed parity check matrix is a parity check matrixused for the same LDPC code. Therefore, a case in which the order ofnumbers in the sequence corresponding to the i^(th) column group inTables 4 to 8 is changed is also covered by the present inventiveconcept.

In addition, even when an arrangement order of sequences correspondingto each column group shown in Tables 4 to 8 is changed, cyclecharacteristics on a graph of the LDPC code and algebraiccharacteristics such as degree distribution are not changed. Therefore,a case in which the arrangement order of the sequences shown in Tables 4to 8 is changed is also covered by the present inventive concept.

In addition, even when a multiple of Q_(ldpc) is equally added to allsequences corresponding to a certain column group in Tables 4 to 8, thecycle characteristics on the graph of the LDPC code or the algebraiccharacteristics such as degree distribution are not changed. Therefore,a result of equally adding a multiple of Q_(ldpc) to the sequences shownin Tables 4 to 8 is also covered by the present inventive concept.However, it should be noted that, when the resulting value obtained byadding the multiple of Q_(ldpc) to a given sequence is greater than orequal to (N_(ldpc)−K_(ldpc)), a value obtained by applying a modulooperation for (N_(ldpc)−K_(ldpc)) to the resulting value should beapplied instead.

Once positions of the rows where 1 exists in the 0^(th) column of thei^(th) column group of the information word submatrix 210 are defined asshown in Tables 4 to 8, positions of rows where 1 exists in anothercolumn of each column group may be defined since the positions of therows where 1 exists in the 0^(th) column are cyclic-shifted by Q_(ldpc)in the next column.

For example, in the case of Table 4, in the 0^(th) column of the 0^(th)column group of the information word submatrix 210, 1 exists in the1606^(th) row, 3402^(nd) row, 4961^(st) row, . . . .

In this case, sinceQ_(ldpc)=(N_(ldpc)−K_(ldpc))/M=(64800−25920)/360=108, the indexes of therows where 1 is located in the 1^(st) column of the 0^(th) column groupmay be 1714=1606+108), 3510(=3402+108), 5069(=4961+108), . . . , and theindexes of the rows where 1 is located in the 2^(nd) column of the0^(th) column group may be 1822(=1714+108), 3618(=3510+108),5177(=5069+108) . . . .

In the above-described method, the indexes of the rows where 1 islocated in all columns of each column group may be defined.

The parity submatrix 220 of the parity check matrix 200 shown in FIG. 2may be defined as follows:

The parity submatrix 220 includes N_(ldpc)−K_(ldpc) number of columns(that is, K_(ldpc) ^(th) column to (N_(ldpc)−1)^(th) column), and has adual diagonal or staircase configuration. Accordingly, the degree ofcolumns except the last column (that is, (N_(ldpc)−1)^(th) column) fromamong the columns included in the parity submatrix 220 is 2, and thedegree of the last column is 1.

As a result, the information word submatrix 210 of the parity checkmatrix 200 may be defined by Tables 4 to 8, and the parity submatrix 220of the parity check matrix 200 may have a dual diagonal configuration.

When the columns and rows of the parity check matrix 200 shown in FIG. 2are permutated based on Equation 4 and Equation 5, the parity checkmatrix shown in FIG. 2 may be changed to a parity check matrix 300 shownin FIG. 3 .Q _(ldpc) ·i+j⇒M·j+i(0≤i<M,0≤j<Q _(ldpc))  (4)K _(ldpc) +Q _(ldpc) ·k+l⇒K _(ldpc) +M·l+k(0≤k<M,0≤1<Q _(ldpc))  (5)

The method for permutating based on Equation 4 and Equation 5 will beexplained below. Since row permutation and column permutation apply thesame principle, the row permutation will be explained by the way of anexample.

In the case of the row permutation, regarding the X^(th) row, i and jsatisfying X=Q_(ldpc)=i+j are calculated and the X^(th) row ispermutated by assigning the calculated i and j to M×j+i. For example,regarding the 7^(th) row, i and j satisfying 7=2×i+j are 3 and 1,respectively. Therefore, the 7^(th) row is permutated to the 13^(th) row(10×1+3=13).

When the row permutation and the column permutation are performed in theabove-described method, the parity check matrix of FIG. 2 may beconverted into the parity check matrix of FIG. 3 .

Referring to FIG. 3 , the parity check matrix 300 is divided into aplurality of partial blocks, and a quasi-cyclic matrix of M×Mcorresponds to each partial block.

Accordingly, the parity check matrix 300 having the configuration ofFIG. 3 is formed of matrix units of M×M. That is, the submatrices of M×Mare arranged in the plurality of partial blocks, constituting the paritycheck matrix 300.

Since the parity check matrix 300 is formed of the quasi-cyclic matricesof M×M, M number of columns may be referred to as a column block and Mnumber of rows may be referred to as a row block. Accordingly, theparity check matrix 300 having the configuration of FIG. 3 is formed ofN_(qc_column)=N_(ldpc)/M number of column blocks andN_(qc_row)=N_(parity)/M number of row blocks.

Hereinafter, the submatrix of M×M will be explained.

First, the (N_(qc_column)−1)^(th) column block of the 0^(th) row block A330 has the format of Equation 6 presented below:

$\begin{matrix}{A = \begin{bmatrix}0 & 0 & \ldots & 0 & 0 \\1 & 0 & \ldots & 0 & 0 \\0 & 1 & \ldots & 0 & 0 \\\vdots & \vdots & \vdots & \vdots & \vdots \\0 & 0 & \ldots & 1 & 0\end{bmatrix}} & (6)\end{matrix}$

As described above, A 330 is an M×M matrix, values of the 0^(th) row andthe (M−1)^(th) column are all “0”, and, regarding 0≤i≤(M−2), the(i+1)^(th) row of the i^(th) column is “1” and the other values are “0”.

Second, regarding 0≤i≤(N_(ldpc)−K_(ldpc))/M−1 in the parity submatrix320, the i^(th) row block of the (K_(ldpc)/M+i)^(th) column block isconfigured by a unit matrix I_(M×M) 340. In addition, regarding0≤i≤(N_(ldpc)−K_(ldpc))/M−2, the (i+1)^(th) row block of the(K_(ldpc)/M+i)^(th) column block is configured by a unit matrix I_(M×M)340.

Third, a block 350 constituting the information word submatrix 310 mayhave a cyclic-shifted format of a cyclic matrix P^(a) ^(ij) , or anadded format of the cyclic-shifted matrix P^(a) ^(ij) of the cyclicmatrix P (or an overlapping format).

For example, a format in which the cyclic matrix P is cyclic-shifted tothe right by 1 may be expressed by Equation 7 presented below:

$\begin{matrix}{P = \begin{bmatrix}0 & 1 & 0 & \; & 0 \\0 & 0 & 1 & \ldots & 0 \\\vdots & \vdots & \vdots & \; & \vdots \\0 & 0 & 0 & \ldots & 1 \\1 & 0 & 0 & \; & 0\end{bmatrix}} & (7)\end{matrix}$

The cyclic matrix P is a square matrix having an M×M size and is amatrix in which a weight of each of M number of rows is 1 and a weightof each of M number of columns is 1. When a_(ij) is 0, the cyclic matrixP, that is, P⁰ indicates a unit matrix I_(M×M), and when a_(ij) is ∞,P^(∞) is a zero matrix.

A submatrix existing where the i^(th) row block and the j^(th) columnblock intersect in the parity check matrix 300 of FIG. 3 may be P^(a)^(ij) . Accordingly, i and j indicate the number of row blocks and thenumber of column blocks in the partial blocks corresponding to theinformation word. Accordingly, in the parity check matrix 300, the totalnumber of columns is N_(ldpc)=M×N_(qc_column), and the total number ofrows is N_(parity)=M×N_(qc_row). That is, the parity check matrix 300 isformed of N_(qc_column) number of “column blocks” and N_(qc_row) numberof “row blocks”.

Hereinafter, a method for performing LDPC encoding based on the paritycheck matrix 200 as shown in FIG. 2 will be explained. An LDPC encodingprocess when the parity check matrix 200 is defined as shown in Table 4by way of an example will be explained for the convenience ofexplanation.

First, when information word bits having the length of K_(ldpc) are [i₀,i₁, i₂, . . . , i_(L) _(ldpc) ⁻¹], and parity bits having the length ofN_(ldpc)−K_(ldpc) are [p₀, p₁, p₂, . . . p_(N) _(ldpc) _(−K) _(ldpc)⁻¹], the LDPC encoding is performed by the following process.

Step 1) Parity bits are initialized as ‘0’. That is, p₀=p₁=p₂= . . .=p_(N) _(ldpc) _(−K) _(ldpc) ⁻¹=0.

Step 2) The 0^(th) information word bit i₀ is accumulated in a paritybit having the address of the parity bit defined in the first row (thatis, the row of i=0) of Table 4 as the index of the parity bit. This maybe expressed by Equation 8 presented below:P ₁₆₀₆ =P ₁₆₀₆ ⊕i ₀P ₃₄₀₂ =P ₃₄₀₂ ⊕i ₀P ₄₉₆₁ =P ₄₉₆₁ ⊕i ₀P ₅₇₅₁ =P ₅₇₅₁ ⊕i ₀P ₇₁₃₂ =P ₇₁₃₂ ⊕i ₀P ₁₁₅₁₆ =P ₁₁₅₁₆ ⊕i ₀P ₁₂₃₀₀ =P ₁₂₃₀₀ ⊕i ₀P ₁₂₄₈₂ =P ₁₂₄₈₂ ⊕i ₀P ₁₂₅₉₂ =P ₁₂₅₉₂ ⊕i ₀P ₁₃₃₄₂ =P ₁₃₃₄₂ ⊕i ₀P ₁₃₇₆₄ =P ₁₃₇₆₄ ⊕i ₀P ₁₄₁₂₃ =P ₁₄₁₂₃ ⊕i ₀P ₂₁₅₇₆ =P ₂₁₅₇₆ ⊕i ₀P ₂₃₉₄₆ =P ₂₃₉₄₆ ⊕i ₀P ₂₄₅₃₃ =P ₂₄₅₃₃ ⊕i ₀P ₂₅₃₇₆ =P ₂₅₃₇₆ ⊕i ₀P ₂₅₆₆₇ =P ₂₅₆₆₇ ⊕i ₀P ₂₆₈₃₆ =P ₂₆₈₃₆ ⊕i ₀P ₃₁₇₉₉ =P ₃₁₇₉₉ ⊕i ₀P ₃₄₁₇₃ =P ₃₄₁₇₃ ⊕i ₀P ₃₅₄₆₂ =P ₃₅₄₆₂ ⊕i ₀P ₃₆₁₅₃ =P ₃₆₁₅₃ ⊕i ₀P ₃₆₇₄₀ =P ₃₆₇₄₀ ⊕i ₀P ₃₇₀₈₅ =P ₃₇₀₈₅ ⊕i ₀P ₃₇₁₅₂ =P ₃₇₁₅₂ ⊕i ₀P ₃₇₄₆₈ =P ₃₇₄₆₈ ⊕i ₀P ₃₇₆₅₈ =P ₃₇₆₅₈ ⊕i ₀  (8)

Herein, i₀ is a 0^(th) information word bit, p_(i) is an i^(th) paritybit, and ⊕ is a binary operation. According to the binary operation, 1⊕1equals 0, 1⊕0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.

Step 3) The other 359 information word bits i_(m) (m=1, 2, . . . , 359)are accumulated in the parity bit. The other information word bits maybelong to the same column group as that of i₀. In this case, the addressof the parity bit may be determined based on Equation 9 presented below:(x+(m mod 360)×Q _(ldpc))mod(N _(ldpc) −K _(ldpc))  (9)

In the above, x is an address of a parity bit accumulator correspondingto the information word bit i₀, and Q_(ldpc) is a size by which eachcolumn is cyclic-shifted in the information word submatrix, and may be108 in the case of Table 4. In addition, since m=1, 2, . . . , 359, (mmod 360) in Equation 9 may be regarded as m.

As a result, information word bits i_(m) (m=1, 2, . . . , 359) areaccumulated in the parity bits having addresses of the parity bitscalculated based on Equation 9 as the indexes, respectively. Forexample, an operation as shown in Equation 10 presented below may beperformed for the information word bit i₁:P ₁₇₁₄ =P ₁₇₁₄ ⊕i ₁P ₃₅₁₀ =P ₃₅₁₀ ⊕i ₁P ₅₀₆₉ =P ₅₀₆₉ ⊕i ₁P ₆₈₅₉ =P ₆₈₅₉ ⊕i ₁P ₇₂₄₀ =P ₇₂₄₀ ⊕i ₁P ₁₁₆₂₄ =P ₁₁₆₂₄ ⊕i ₁P ₁₂₄₀₈ =P ₁₂₄₀₈ ⊕i ₁P ₁₂₅₉₀ =P ₁₂₅₉₀ ⊕i ₁P ₁₂₇₀₀ =P ₁₂₇₀₀ ⊕i ₁P ₁₃₄₅₀ =P ₁₃₄₅₀ ⊕i ₁P ₁₃₈₇₂ =P ₁₃₈₇₂ ⊕i ₁P ₁₄₂₃₁ =P ₁₄₂₃₁ ⊕i ₁P ₂₁₆₈₄ =P ₂₁₆₈₄ ⊕i ₁P ₂₄₀₅₄ =P ₂₄₀₅₄ ⊕i ₁P ₂₄₆₄₁ =P ₂₄₆₄₁ ⊕i ₁P ₂₅₄₈₄ =P ₂₅₄₈₄ ⊕i ₁P ₂₅₇₇₅ =P ₂₅₇₇₅ ⊕i ₁P ₂₆₉₄₄ =P ₂₆₉₄₄ ⊕i ₁P ₃₁₉₀₇ =P ₃₁₉₀₇ ⊕i ₁P ₃₄₂₈₁ =P ₃₄₂₈₁ ⊕i ₁P ₃₅₅₇₀ =P ₃₅₅₇₀ ⊕i ₁P ₃₆₂₆₁ =P ₃₆₂₆₁ ⊕i ₁P ₃₆₈₄₈ =P ₃₆₈₄₈ ⊕i ₁P ₃₇₁₉₃ =P ₃₇₁₉₃ ⊕i ₁P ₃₇₂₆₀ =P ₃₇₂₆₀ ⊕i ₁P ₃₇₅₇₆ =P ₃₇₅₇₆ ⊕i ₁P ₃₇₇₆₆ =P ₃₇₇₆₆ ⊕i ₁  (10)

Herein, i₁ is a 1^(st) information word bit, p_(i) is an ith parity bit,and ⊕ is a binary operation. According to the binary operation, 1⊕1equals 0, 1⊕0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.

Step 4) The 360^(th) information word bits i₃₆₀ is accumulated in aparity bit having an address of the parity bit defined in the 2^(nd) row(that is, the row of i=1) of Table 4 as the index of the parity bit.

Step 5) The other 359 information word bits belonging to the same groupas that of the information word bit i₃₆₀ are accumulated in the paritybit. In this case, the address of the parity bit may be determined basedon Equation 9. However, in this case, x is the address of the parity bitaccumulator corresponding to the information word bit i₃₆₀.

Step 6) Steps 4 and 5 described above are repeated for all of the columngroups of Table 4.

Step 7) As a result, a parity bit p_(i) is calculated based on Equation11 presented below. In this case, i is initialized as 1.p _(i) =p _(i) ⊕p _(i−1) i=1,2, . . . ,N _(ldpc) −K _(ldpc)−1  (11)

In Equation 11, p_(i) is an ith parity bit, N_(ldpc) is a length of anLDPC codeword, K_(ldpc) is a length of an information word of the LDPCcodeword, and ⊕ is a binary operation.

As a result, the encoder 110 may calculate the parity bits according tothe above-described method.

Referring back to FIG. 1 , the encoder 110 may perform the LDPC encodingby using various code rates such as 3/15, 4/15, 5/15, 6/15, 7/15, 8/15,9/15, 10/15, 11/15, 12/15, 13/15, etc. In addition, the encoder 110 maygenerate an LDPC codeword having various lengths such as 16200, 64800,etc., based on the length of the information word bits and the coderate.

In this case, the encoder 110 may perform the LDPC encoding by using theparity check matrix having the information word submatrix defined byTables 4 to 8 and the parity submatrix having the dual diagonalconfiguration (that is, the parity check matrix shown in FIG. 2 ), ormay perform the LDPC encoding by using the parity check matrix which isrow and column permutated from the parity check matrix of FIG. 2 basedon Equation 4 and Equation 5 (that is, the parity check matrix havingthe configuration of FIG. 3 ).

In addition, the encoder 110 may perform Bose, Chaudhuri, Hocquenghem(BCH) encoding as well as the LDPC encoding. To achieve this, theencoder 110 may further include a BCH encoder (not shown) to perform BCHencoding.

In this case, the encoder 110 may perform encoding in an order of BCHencoding and LDPC encoding. Specifically, the encoder 110 may add BCHparity bits to input bits by performing BCH encoding and LDPC-encodesthe information word bits including the input bits and the BCH paritybits, thereby generating an LDPC codeword.

The interleaver 120 interleaves the LDPC codeword. That is, theinterleaver 120 receives the LDPC codeword from the encoder 110, andinterleaves the LDPC codeword based on various interleaving rules.

In particular, the interleaver 120 may interleave the LDPC codeword suchthat a bit included in a predetermined bit group from among a pluralityof bit groups constituting the LDPC codeword (that is, a plurality ofgroups or a plurality of blocks) is mapped onto a predetermined bit of amodulation symbol. Accordingly, the modulator 130 may map the bitincluded in the predetermined group from among the plurality of bitgroups constituting the LDPC codeword onto the predetermined bit of themodulation symbol.

Hereinafter, the interleaving rules used in the interleaver 120 will beexplained in detail according to cases.

Exemplary Embodiment 1: Case in which a Block Interleaver is Used

According to a first exemplary embodiment, the interleaver 120 mayinterleave the LDPC codeword in the method as described below, such thatthe bit included in a predetermined bit group from among the pluralityof bit groups constituting the interleaved LDPC codeword is mapped ontoa predetermined bit of a modulation symbol. This will be explained belowin detail with reference to FIG. 4 .

FIG. 4 is a block diagram to illustrate the a configuration of aninterleaver according to an exemplary embodiment. Referring to FIG. 4 ,the interleaver 120 may include a parity interleaver 121, a groupinterleaver 122 (or a group-wise interleaver 122), a group twistinterleaver 123 and a block interleaver 124.

The parity interleaver 121 interleaves the parity bits constituting theLDPC codeword.

Specifically, when the LDPC codeword is generated based on the paritycheck matrix 200 having the configuration of FIG. 2 , the parityinterleaver 121 may interleave only the parity bits of the LDPCcodeword, among the information word bits and the parity bits of theLDPC codeword, by using Equations 12 presented below:u _(i) =c _(i) for 0≤i<K _(ldpc), andu _(K) _(ldpc) _(+M·t+s) =c _(K) _(ldpc) _(+Q) _(ldpc) _(·s+t) for0≤s<M,0≤t<Q _(ldpc)  (12),where M is an interval at which a pattern of a column group is repeatedin the information word submatrix 210, that is, the number of columnsincluded in a column group (for example, M=360), and Q_(ldpc) is a sizeby which each column is cyclic-shifted in the information word submatrix210. That is, the parity interleaver 121 performs parity interleavingwith respect to the LDPC codeword c=(c₀, c₁, . . . , c_(N) _(ldpc) ⁻¹),and outputs U=(u₀, u₁, u_(N) _(ldpc) ⁻¹).

The LDPC codeword which is parity-interleaved in the above-describedmethod may be configured such that a predetermined number of continuousbits of the LDPC codeword have similar decoding characteristics (cycledistribution, a degree of a column, etc.).

For example, the LDPC codeword may have the same characteristics on thebasis of M number of continuous bits. Herein, M is an interval at whicha pattern of a column group is repeated in the information wordsubmatrix 210 and, for example, may be 360.

Specifically, a product of the LDPC codeword bits and the parity checkmatrix should be “0”. This means that a sum of products of the i^(th)LDPC codeword bit, c_(i) (i=0, 1, . . . , N_(ldpc)−1) and the i^(th)column of the parity check matrix should be a “0” vector. Accordingly,the i^(th) LDPC codeword bit may be regarded as corresponding to thei^(th) column of the parity check matrix.

In the case of the parity check matrix 200 of FIG. 2 , M number ofcolumns in the information word submatrix 210 belong to the same groupand the information word submatrix 210 has the same characteristics onthe basis of a column group (for example, the columns belonging to thesame column group have the same degree distribution and the same cyclecharacteristic).

In this case, since M number of continuous bits in the information wordbits correspond to the same column group of the information wordsubmatrix 210, the information word bits may be formed of M number ofcontinuous bits having the same codeword characteristics. When theparity bits of the LDPC codeword are interleaved by the parityinterleaver 121, the parity bits of the LDPC codeword may be formed of Mnumber of continuous bits having the same codeword characteristics.

However, regarding the LDPC codeword encoded based on the parity checkmatrix 300 of FIG. 3 , parity interleaving may not be performed. In thiscase, the parity interleaver 121 may be omitted.

The group interleaver 122 may divide the parity-interleaved LDPCcodeword into a plurality of bit groups and rearrange the order of theplurality of bit groups in bits group wise (group units). That is, thegroup interleaver 122 may interleave the plurality of bit groups in bitsgroup wise.

To achieve this, the group interleaver 122 divides theparity-interleaved LDPC codeword into a plurality of bit groups by usingEquation 13 or Equation 14 presented below.

$\begin{matrix}{\mspace{79mu}{X_{j} = {{\left\{ {{\left. u_{k} \middle| j \right. = \left\lfloor \frac{k}{360} \right\rfloor},{0 \leq k < N_{ldpc}}} \right\}{for}\; 0} \leq j < N_{group}}}} & (13) \\{X_{j} = {{\left\{ {\left. u_{k} \middle| {{360 \times j} \leq k < {360 \times \left( {j + 1} \right)}} \right.,{0 \leq k < N_{ldpc}}} \right\} for0} \leq j < N_{group}}} & (14)\end{matrix}$where N_(group) is the total number of bit groups, X_(j) is the i^(th)bit group, and u_(k) is the k^(th) LDPC codeword bit input to the groupinterleaver 122. In addition,

$\left\lfloor \frac{k}{360} \right\rfloor$is the largest integer below k/360.

Since 360 in these equations indicates an example of the interval M atwhich the pattern of a column group is repeated in the information wordsubmatrix, 360 in these equations can be changed to M.

The LDPC codeword which is divided into the plurality of bit groups maybe expressed as shown in FIG. 5 .

Referring to FIG. 5 , the LDPC codeword is divided into the plurality ofbit groups and each bit group is formed of M number of continuous bits.When M is 360, each of the plurality of bit groups may be formed of 360bits. Accordingly, each of the bit groups may be formed of bitscorresponding to each of the column groups of the parity check matrix.

Specifically, since the LDPC codeword is divided by M number ofcontinuous bits, K_(ldpc) number of information word bits are dividedinto (K_(ldpc)/M) number of bit groups, and N_(ldpc)−K_(ldpc) number ofparity bits are divided into (N_(ldpc)−K_(ldpc))/M number of bit groups.Accordingly, the LDPC codeword may be divided into (N_(ldpc)/M) numberof bit groups in total.

For example, when M=360 and the length N_(ldpc) of the LDPC codeword is64800, the number of bit groups N_(groups) is 180 (=64800/360), and,when the length N_(ldpc) of the LDPC codeword is 16200, the number ofbit groups N_(group) is 45 (16200/360).

As described above, the group interleaver 122 divides the LDPC codewordsuch that M number of continuous bits are included in a same group sincethe LDPC codeword has the same codeword characteristics on the basis ofM number of continuous bits. Accordingly, when the LDPC codeword isgrouped by M number of continuous bits, the bits having the samecodeword characteristics belong to the same group.

In the above-described example, the number of bits constituting each bitgroup is M. However, this is merely an example and the number of bitsconstituting each bit group is variable.

For example, the number of bits constituting each bit group may be analiquot part of M. That is, the number of bits constituting each bitgroup may be an aliquot part of the number of columns constituting acolumn group of the information word submatrix of the parity checkmatrix. In this case, each bit group may be formed of an aliquot part ofM number of bits. For example, when the number of columns constituting acolumn group of the information word submatrix is 360, that is, M=360,the group interleaver 122 may divide the LDPC codeword into a pluralityof bit groups such that the number of bits constituting each bit groupis one of the aliquot parts of 360.

In the following explanation, the number of bits constituting a bitgroup is M by way of an example, for the convenience of explanation.

Thereafter, the group interleaver 122 interleaves the LDPC codeword inbits group wise. Specifically, the group interleaver 122 may group theLDPC codeword into the plurality of bit groups and rearrange theplurality of bit groups in bits group wise. That is, the groupinterleaver 122 changes positions of the plurality of bit groupsconstituting the LDPC codeword and rearranges the order of the pluralityof bit groups constituting the LDPC codeword in bits group wise.

According to an exemplary embodiment, the group interleaver 122 mayrearrange the order of the plurality of bit groups in bits group wisesuch that bit groups including bits mapped onto a same modulation symbolfrom among the plurality of bit groups are spaced apart from one anotherat a predetermined interval.

In this case, the group interleaver 122 may rearrange the order of theplurality of bit groups in bits group wise by considering at least oneof the number of rows and columns of the block interleaver 124, thenumber of bit groups of the LDPC codeword, and the number of bitsincluded in each bit group, such that bit groups including bits mappedonto the same modulation symbol are spaced apart from one another at thepredetermined interval.

To achieve this, the group interleaver 122 may rearrange the order ofthe plurality of bit groups in bits group wise by using Equation 15presented below:Y _(j) =X _(π(j))(0≤j<N _(group))  (15),where X_(j) is the j^(th) bit group before group interleaving, and Y_(j)is the j^(th) bit group after group interleaving. In addition, π(j) is aparameter indicating an interleaving order and is determined by at leastone of a length of an LDPC codeword, a code rate, and a modulationmethod. That is, π(j) denotes a permutation order for group wiseinterleaving.

Accordingly, X_(π(j)) is a π(j)^(th) bit group before groupinterleaving, and Equation 15 means that the pre-interleaving π(j)^(th)bit group is interleaved into the j^(th) bit group.

According to an exemplary embodiment, an example of π(j) may be definedas in Tables 9 to 13 presented below.

In this case, π(j) is defined according to a length of an LPDC codewordand a code rate, and a parity check matrix is also defined according toa length of an LDPC codeword and a code rate. Accordingly, when LDPCencoding is performed based on a specific parity check matrix accordingto a length of an LDPC codeword and a code rate, the LDPC codeword maybe interleaved in bits group wise based on π(j) satisfying thecorresponding length of the LDPC codeword and code rate.

For example, when the encoder 110 performs LDPC encoding at a code rateof 6/15 to generate an LDPC codeword of a length of 64800, the groupinterleaver 122 may perform interleaving by using π(j) which is definedaccording to the length of the LDPC codeword of 64800 and the code rateof 6/15 in Tables 9 to 13 presented below, for example, by using π(j)defined as shown in Table 9.

For example, when the length N_(ldpc) of the LDPC codeword is 64800, thecode rate is 6/15, and the modulation method is 1024-QuadratureAmplitude Modulation (QAM), π(j) may be defined as in Table 9 presentedbelow.

TABLE 9 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 66 21 51 55 54 24 33 12 70 63 47 65 block of 56 2 43 64 58 67 5368 61 39 52 69 Group-wise 25 44 136 29 36 26 126 177 15 37 148 9interleaver 178 28 34 106 127 76 131 105 138 75 130 101 input, 143 81 3296 3 78 107 86 98 16 162 150 144 151 90 11 156 100 175 83 155 159 128 88141 129 146 122 73 112 132 125 174 169 168 79 104 134 82 95 133 164 154120 110 170 114 153 Order of bits group to be block interleaved π(j) (0≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 3536 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 6768 output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 1458 0 57 23 71 59 14 40 42 62 block of 1 22 31 161 38 30 19 17 18 4 41Group-wise 13 45 46 152 50 49 27 77 60 35 48 interleaver 167 117 173 113108 92 135 124 121 97 149 input, 111 158 172 139 74 142 166 7 5 119 2087 93 103 94 140 165 6 137 157 10 85 84 118 179 147 91 160 163 115 89 80102 72 109 171 176 99 116 123

In the case of Table 9, Equation 15 may be expressed as Y₀=X_(π(0))=X₆₆,Y₁=X_(π(1))=X₂₁, Y₂=X_(π(2))=X₅₁, . . . , Y₁₇₈=X_(π(178))=X₁₁₆, andY₁₇₉=X_(π(179))=X₁₂₃. Accordingly, the group interleaver 122 mayrearrange the order of the plurality of bit groups in bits group wise bychanging the 66^(th) bit group to the 0^(th) bit group, the 21^(st) bitgroup to the 1^(st) bit group, the 51^(st) bit group to the 2^(nd) bitgroup, . . . , the 116^(th) bit group to the 178^(th) bit group, and the123^(rd) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 8/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 10 presented below.

TABLE 10 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 77 48 82 51 57 69 65 6 71 90 84 81 block of 18 38 89 49 93 36 6447 40 42 76 70 Group-wise 87 67 86 10 1 58 17 14 175 91 68 85interleaver 83 46 44 102 30 112 122 110 29 20 105 138 input, 28 26 45 2423 21 157 98 35 95 22 32 159 155 179 160 161 130 123 172 139 124 153 0148 158 129 163 176 151 171 8 106 144 150 169 142 104 115 135 121 100 12170 156 126 5 127 Order of bits group to be block interleaved π(j) (0 ≤j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 3637 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 50 88 6155 53 73 39 13 79 75 41 block of 56 3 72 2 54 52 145 19 78 80 63Group-wise 94 15 43 74 60 66 37 92 4 9 16 interleaver 101 174 33 137 136131 166 59 34 62 125 input, 103 27 113 31 119 173 168 118 120 114 149109 167 128 107 117 147 177 96 164 152 11 108 162 143 111 141 133 178134 146 99 132 154 97 140 116 165 7 25

In the case of Table 10, Equation 15 may be expressed asY₀=X_(π(0))=X₇₇, Y₁=X_(π(1))=X₄₈, Y₂=X_(π(2))=X₈₂, . . . ,Y₁₇₈=X_(π(178))=X₇, and Y₁₇₉=X_(π(179))=X₂₅. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 77^(th) bit group to the 0^(th) bitgroup, the 48^(th) bit group to the 1^(st) bit group, the 82^(nd) bitgroup to the 2^(nd) bit group, . . . , the 7^(th) bit group to the178^(th) bit group, and the 25^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 10/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 11 presented below. In particular, whenthe encoder 110 performs LDPC encoding based on the parity check matrixdefined by Table 6, the group interleaver 122 may perform groupinterleaving by using π(j) defined as in Table 11 presented below:

TABLE 11 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 7 58 108 59 1 14 54 115 57 29 64 65 block of 71 106 50 44 15 524 100 90 111 77 89 Group-wise 103 30 105 76 107 88 95 28 66 102 25 39interleaver 86 45 119 23 79 35 72 33 98 40 38 24 input, 41 97 2 21 61117 70 62 34 11 67 37 69 139 133 154 160 128 168 84 171 162 31 43 134126 18 129 137 74 148 147 167 136 164 146 150 16 172 3 155 169 142 156120 122 19 144 Order of bits group to be block interleaved π(j) (0 ≤ j <180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 3738 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 8 101113 60 46 104 87 9 93 81 94 block of 92 5 82 10 116 109 75 91 47 80 99Group-wise 78 53 118 112 0 83 22 36 51 55 85 interleaver 63 73 20 48 2796 68 26 110 42 12 input, 49 114 56 32 149 163 173 159 132 170 179 135123 178 130 127 145 157 176 177 140 151 153 138 161 6 143 124 17 174 131175 165 158 13 152 141 166 125 121

In the case of Table 11, Equation 15 may be expressed as Y₀=X_(π(0))=X₇,Y₁=X_(π(1))=X₅₈, Y₂=X_(π(2))=X₁₀₈, . . . , Y₁₇₈=X_(π(178))=X₁₂₅, andY₁₇₉=X_(π(179))=X₁₂₁. Accordingly, the group interleaver 122 mayrearrange the order of the plurality of bit groups in bits group wise bychanging the 7^(th) bit group to the 0^(th) bit group, the 58^(th) bitgroup to the 1^(st) bit group, the 108^(th) bit group to the 2^(nd) bitgroup, . . . , the 125^(th) bit group to the 178^(th) bit group, and the121^(st) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 10/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 12 presented below. In particular, whenthe encoder 110 performs LDPC encoding based on the parity check matrixdefined by Table 7, the group interleaver 122 may perform groupinterleaving by using π(j) defined as in Table 12 presented below:

TABLE 12 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 111 45 78 97 75 63 35 15 9 25 39 94 block of 68 98 31 107 19 11048 58 71 87 43 62 Group-wise 1 17 61 55 90 56 14 47 77 2 117 20interleaver 116 29 26 54 38 60 114 59 105 67 103 0 input, 42 51 40 119 821 81 76 112 28 34 36 142 141 136 157 162 123 159 150 171 174 137 65 13552 170 138 127 96 165 156 148 179 163 3 16 144 128 11 175 134 124 130146 161 145 120 Order of bits group to be block interleaved π(j) (0 ≤ j< 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 3637 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 24 84100 49 44 41 32 101 82 23 79 block of 85 70 95 57 10 50 99 118 73 27 12Group-wise 74 106 83 102 109 113 72 88 115 37 30 interleaver 80 64 4 9166 46 108 33 104 93 7 input, 86 69 92 53 122 126 131 160 154 6 22 13 177166 139 167 172 176 153 89 152 168 133 143 121 132 169 147 173 155 149178 158 129 164 125 5 151 18 140

In the case of Table 12, Equation 15 may be expressed asY₀=X_(π(0))=X₁₁₁, Y₁=X_(π(1))=X₄₅, Y₂=X_(π(2))=X₇₈, . . . ,Y₁₇₈=X_(π(178))=X₁₈, and Y₁₇₉=X_(π(179))=X₁₄₀. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 111^(th) bit group to the 0^(th) bitgroup, the 45^(th) bit group to the 1^(st) bit group, the 78^(th) bitgroup to the 2^(nd) bit group, . . . , the 18^(th) bit group to the178^(th) bit group, and the 140^(th) bit group to the 179^(th) bitgroup.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 12/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 13 presented below.

TABLE 13 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 91 19 11 106 14 40 20 67 32 22 31 23 block of 133 4 2 21 122 3812 69 111 81 82 58 Group-wise 80 76 138 87 85 65 130 57 102 83 64 86interleaver 30 45 94 26 116 98 37 55 44 70 25 7 input, 29 62 50 139 56109 77 59 127 142 96 105 178 129 18 131 42 165 101 134 36 140 132 103 63107 162 157 66 104 17 147 167 174 179 3 16 15 148 5 146 163 172 175 151169 176 150 Order of bits group to be block interleaved π(j) (0 ≤ j <180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 3738 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 78 68 79141 117 95 88 136 52 121 1 block of 46 112 60 33 73 53 92 75 48 47 110Group-wise 100 39 49 125 108 119 6 118 35 61 71 interleaver 34 114 135128 137 84 51 28 97 27 89 input, 99 90 13 124 120 115 126 143 149 74 4172 164 93 54 166 43 123 113 0 154 10 173 160 155 161 152 156 177 24 1709 159 153 171 158 168 144 8 145

In the case of Table 13, Equation 15 may be expressed asY₀=X_(π(0))=X₉₁, Y₁=X_(π(1))=X₁₉, Y₂=X_(π(2))=X₁₁, . . . ,Y₁₇₈=X_(π(178))=X₈, and Y₁₇₉=X_(π(179))=X₁₄₅. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 91^(st) bit group to the 0^(th) bitgroup, the 19^(th) bit group to the 1^(st) bit group, the 11^(th) bitgroup to the 2^(nd) bit group, . . . , the 8^(th) bit group to the178^(th) bit group, and the 145^(th) bit group to the 179^(th) bitgroup.

In the above-described examples, the length of the LDPC codeword is64800 and the code rate is 6/15, 8/15, 10/15, and 12/15. However, thisis merely an example and the interleaving pattern may be definedvariously when the length of the LDPC codeword is 16200 or the code ratehas different values.

As described above, the group interleaver 122 may rearrange the order ofthe plurality of bit groups in bits group wise by using Equation 15 andTables 9 to 13.

“j-th block of Group-wise Interleaver output” in Tables 9 to 13indicates the j-th bit group output from the group interleaver 122 afterinterleaving, and “π(j)-th block of Group-wise Interleaver input”indicates the π(j)-th bit group input to the group interleaver 122.

In addition, since the order of the bit groups constituting the LDPCcodeword is rearranged by the group interleaver 122 in bits group wise,and then the bit groups are block-interleaved by the block interleaver124, which will be described below, “Order of bits groups to be blockinterleaved” is set forth in Tables 9 to 13 in relation to π(j).

π(j) defined as shown in Tables 9 to 13 may be arranged according to thecode rates as shown in Table 14 presented below:

TABLE 14 (CR 6/15) (CR 8/15) (CR 10/15) (CR 10/15) (CR 12/15) j-th blockof π(j)-th block of π(j)-th block of π(j)-th block of π(j)-th block ofπ(j)-th block of Group-wise Group-wise Group-wise Group-wise Group-wiseGroup-wise Interleaver Interleaver Interleaver Interleaver InterleaverInterleaver output input input input input input 0 66 77 7 111 91 1 2148 58 45 19 2 51 82 108 78 11 3 55 51 59 97 106 4 54 57 1 75 14 5 24 6914 63 40 6 33 65 54 35 20 7 12 6 115 15 67 8 70 71 57 9 32 9 63 90 29 2522 10 47 84 64 39 31 11 65 81 65 94 23 12 145 50 8 24 78 13 8 88 101 8468 14 0 61 113 100 79 15 57 55 60 49 141 16 23 53 46 44 117 17 71 73 10441 95 18 59 39 87 32 88 19 14 13 9 101 136 20 40 79 93 82 52 21 42 75 8123 121 22 62 41 94 79 1 23 56 18 71 68 133 24 2 38 106 98 4 25 43 89 5031 2 26 64 49 44 107 21 27 58 93 15 19 122 28 67 36 52 110 38 29 53 64 448 12 30 68 47 100 58 69 31 61 40 90 71 111 32 39 42 111 87 81 33 52 7677 43 82 34 69 70 89 62 58 35 1 56 92 85 46 36 22 3 5 70 112 37 31 72 8295 60 38 161 2 10 57 33 39 38 54 116 10 73 40 30 52 109 50 53 41 19 14575 99 92 42 17 19 91 118 75 43 18 78 47 73 48 44 4 80 80 27 47 45 41 6399 12 110 46 25 87 103 1 80 47 44 67 30 17 76 48 136 86 105 61 138 49 2910 76 55 87 50 36 1 107 90 85 51 26 58 88 56 65 52 126 17 95 14 130 53177 14 28 47 57 54 15 175 66 77 102 55 37 91 102 2 83 56 148 68 25 11764 57 9 85 39 20 86 58 13 94 78 74 100 59 45 15 53 106 39 60 46 43 11883 49 61 152 74 112 102 125 62 50 60 0 109 108 63 49 66 83 113 119 64 2737 22 72 6 65 77 92 36 88 118 66 60 4 51 115 35 67 35 9 55 37 61 68 4816 85 30 71 69 178 83 86 116 30 70 28 46 45 29 45 71 34 44 119 26 94 72106 102 23 54 26 73 127 30 79 38 116 74 76 112 35 60 98 75 131 122 72114 37 76 105 110 33 59 55 77 138 29 98 105 44 78 75 20 40 67 70 79 130105 38 103 25 80 101 138 24 0 7 81 167 101 63 80 34 82 117 174 73 64 11483 173 33 20 4 135 84 113 137 48 91 128 85 108 136 27 66 137 86 92 13196 46 84 87 135 166 68 108 51 88 124 59 26 33 28 89 121 34 110 104 97 9097 62 42 93 27 91 149 125 12 7 89 92 143 28 41 42 29 93 81 26 97 51 6294 32 45 2 40 50 95 96 24 21 119 139 96 3 23 61 8 56 97 78 21 117 21 10998 107 157 70 81 77 99 86 98 62 76 59 100 98 35 34 112 127 101 16 95 1128 142 102 162 22 67 34 96 103 150 32 37 36 105 104 111 103 49 86 99 105158 27 114 69 90 106 172 113 56 92 13 107 139 31 32 53 124 108 74 119149 122 120 109 142 173 163 126 115 110 166 168 173 131 126 111 7 118159 160 143 112 5 120 132 154 149 113 119 114 170 6 74 114 20 149 179 2241 115 144 159 69 142 178 116 151 155 139 141 129 117 90 179 133 136 18118 11 160 154 157 131 119 156 161 160 162 42 120 100 130 128 123 165121 175 123 168 159 101 122 83 172 84 150 134 123 155 139 171 171 36 124159 124 162 174 140 125 128 153 31 137 132 126 88 0 43 65 103 127 87 109135 13 72 128 93 167 123 177 164 129 103 128 178 166 93 130 94 107 130139 54 131 140 117 127 167 166 132 165 147 145 172 43 133 6 177 157 176123 134 137 96 176 153 113 135 157 164 177 89 0 136 10 152 140 152 154137 85 11 151 168 10 138 141 148 134 135 63 139 129 158 126 52 107 140146 129 18 170 162 141 122 163 129 138 157 142 73 176 137 127 66 143 112151 74 96 104 144 132 171 148 165 17 145 125 8 147 156 147 146 174 106167 148 167 147 169 144 136 179 174 148 168 150 164 163 179 149 79 169146 3 3 150 84 108 153 133 173 151 118 162 138 143 160 152 179 143 161121 155 153 147 111 6 132 161 154 91 141 143 169 152 155 160 133 124 147156 156 163 178 17 173 177 157 115 134 174 155 24 158 89 146 131 149 170159 80 99 175 178 9 160 102 132 165 158 159 161 104 142 150 16 16 162134 104 16 144 15 163 82 115 172 128 148 164 95 135 3 11 5 165 133 121155 175 146 166 164 100 169 134 163 167 154 12 142 124 172 168 120 170156 130 175 169 110 156 120 146 151 170 170 126 122 161 169 171 114 5 19145 176 172 153 127 144 120 150 173 72 154 158 129 153 174 109 97 13 164171 175 171 140 152 125 158 176 176 116 141 5 168 177 99 165 166 151 144178 116 7 125 18 8 179 123 25 121 140 145

“j-th block of Group-wise Interleaver output” in Table 14 indicates thej-th bit group output from the group interleaver 122 after interleaving,and “π(j)-th block of Group-wise Interleaver input” indicates theπ(j)-th bit group input to the group interleaver 122. Referring to Table14, it can be seen that Table 14 is arrangement of data described inTables 9 to 13 according to the code rates.

The group interleaver 122 may interleave the LDPC codeword in bits groupwise by using Equation 16 presented below:Y _(π(j)) =X _(j)(0≤j<N _(group))  (16),where X_(j) is the j^(th) bit group before group interleaving, and Y_(j)is the j^(th) bit group after group interleaving. In addition, π(j) is aparameter indicating an interleaving order and is determined by at leastone of a length of an LDPC codeword, a code rate, and a modulationmethod.

Accordingly, X_(j) is a j^(th) bit group before group interleaving, andEquation 16 means that the pre-interleaving j^(th) bit group isinterleaved into the π(i)^(th) bit group.

According to another exemplary embodiment, an example of π(j) may bedefined as in Tables 15 to 19 presented below.

In this case, π(j) is defined according to a length of an LPDC codewordand a code rate, and a parity check matrix is also defined according toa length of an LDPC codeword and a code rate. Accordingly, when LDPCencoding is performed based on a specific parity check matrix accordingto a length of an LDPC codeword and a code rate, the LDPC codeword maybe interleaved in bits group wise based on π(j) satisfying thecorresponding length of the LDPC codeword and code rate.

For example, when the encoder 110 performs LDPC encoding at a code rateof 6/15 to generate an LDPC codeword of a length of 64800, the groupinterleaver 122 may perform interleaving by using π(j) which is definedaccording to the length of the LDPC codeword of 64800 and the code rateof 6/15 in Tables 15 to 19 presented below, for example, by using π(j)defined as shown in Table 15.

For example, when the length N_(ldpc) of the LDPC codeword is 64800, thecode rate is 6/15, and the modulation method is 1024-QAM, π(j) may bedefined as in Table 15 presented below.

TABLE 15 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 Intput 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 14 35 24 96 44 112 133 111 13 57 136 118 block of 16 5 46 51 6470 49 40 37 94 6 71 Group-wise 60 10 68 63 62 2 33 29 4 3 23 15interleaver 34 8 17 173 142 108 78 74 65 97 149 159 output, 86 128 130164 95 90 100 177 120 80 160 129 157 178 82 151 113 168 89 141 179 88145 52 77 107 131 138 109 92 115 12 140 153 56 91 38 102 156 166 132 11081 148 147 170 175 106 Order of bits group to be block interleaved π(j)(0 ≤ j < 180) 12 13 14 15 16 17 18 19 20 21 22 j-th block of 35 36 37 3839 40 41 42 43 44 45 Group-wise 58 59 60 61 62 63 64 65 66 67 68interleaver 81 82 83 84 85 86 87 88 89 90 91 Intput 104 105 106 107 108109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179π(j)-th 7 58 19 54 101 42 43 41 114 1 36 block of 67 50 55 39 32 20 4521 25 47 59 Group-wise 27 18 66 31 22 9 26 11 0 28 30 interleaver 93 163122 150 137 99 127 126 158 117 154 output, 161 76 72 98 85 174 169 104143 84 171 73 125 139 79 75 144 165 162 87 48 134 103 116 61 172 167 123119 135 105 124 155 83 146 121 176 53 69 152

In the case of Table 15, Equation 16 may be expressed asX₀=Y_(π(0))=Y₁₄, X₁=Y_(π(1))=Y₃₅, X₂=Y_(π(2))=Y₂₄, . . . ,X₁₇₈=Y_(π(178))=Y₆₉, and X₁₇₉=Y_(π(179))=Y₁₅₂. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 0^(th) bit group to the 14^(th) bitgroup, the 1^(st) bit group to the 35^(th) bit group, the 2^(nd) bitgroup to the 24^(th) bit group, . . . , the 178^(th) bit group to the69^(th) bit group, and the 179^(th) bit group to the 152^(nd) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 8/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 16 presented below.

TABLE 16 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 intput 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 126 50 38 36 66 171 7 178 145 67 49 137 block of 96 95 179 93105 92 77 73 107 103 83 89 Group-wise 70 30 1 26 12 3 40 16 39 15 35 4interleaver 5 34 8 37 17 61 21 33 0 43 20 44 output, 65 27 58 101 134174 99 159 166 81 72 104 163 176 131 111 108 112 165 75 121 124 91 17080 123 175 154 161 152 147 41 158 132 138 114 119 151 141 135 177 87 128110 149 168 144 122 Order of bits group to be block interleaved π(j) (0≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 3536 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 6768 intput 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 16719 53 59 68 52 23 42 78 97 102 block of 100 28 64 24 18 31 22 32 60 7194 Group-wise 51 88 62 14 90 45 29 6 63 47 56 interleaver 11 2 69 10 5748 46 13 25 9 55 output, 162 79 146 130 150 127 76 153 74 106 113 172129 140 120 86 160 155 157 164 85 84 148 143 136 125 173 116 169 98 139115 118 109 82 54 142 133 156 117

In the case of Table 16, Equation 16 may be expressed asX₀=Y_(π(0))=Y₁₂₆, X₁=Y_(π(1))=Y₅₀, X₂=Y_(π(2))=Y₃₈, . . . ,X₁₇₈=Y_(π(178))=Y₁₅₆, and X₁₇₉=Y_(π(179))=Y₁₁₇. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 0^(th) bit group to the 126^(th) bitgroup, the 1^(st) bit group to the 50^(th) bit group, the 2^(nd) bitgroup to the 38^(th) bit group, . . . , the 178^(th) bit group to the156^(th) bit group, and the 179^(th) bit group to the 117^(th) bitgroup.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 10/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 17 presented below. In particular, whenthe encoder 110 performs LDPC encoding based on the parity check matrixdefined by Table 6, the group interleaver 122 may perform groupinterleaving by using π(j) defined as in Table 17 presented below:

TABLE 17 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 62 4 94 164 29 36 153 0 12 19 38 101 block of 72 80 56 88 85 539 47 125 107 76 100 Group-wise 16 43 84 104 25 66 28 59 6 67 106 8interleaver 115 98 23 75 82 143 41 49 33 58 73 44 output, 35 20 22 52 8693 77 45 30 13 55 46 7 39 97 60 71 169 179 170 128 155 178 139 151 116136 176 167 154 172 132 149 145 144 108 152 124 109 148 160 177 146 121166 113 123 163 Order of bits group to be block interleaved π(j) (0 ≤ j< 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 3637 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 91 174 527 162 156 140 171 83 95 64 block of 74 65 103 79 57 78 92 90 126 26 70Group-wise 1 3 15 96 99 81 10 11 54 102 87 interleaver 21 37 63 122 6869 18 51 34 31 42 output, 17 48 24 50 2 40 89 32 61 14 105 131 120 141130 158 112 117 138 127 147 142 161 137 175 150 118 165 168 133 173 111119 110 157 159 134 135 129 114

In the case of Table 17, Equation 16 may be expressed asX₀=Y_(π(0))=Y₆₂, X₁=Y_(π(1))=Y₄, X₂=Y_(π(2))=Y₉₄, . . . ,X₁₇₈=Y_(π(178))=Y₁₂₉, and X₁₇₉=Y_(π(179))=Y₁₁₄. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 0^(th) bit group to the 62^(nd) bitgroup, the 1^(st) bit group to the 4^(th) bit group, the 2^(nd) bitgroup to the 94^(th) bit group, . . . , the 178^(th) bit group to the129^(th) bit group, and the 179^(th) bit group to the 114^(th) bitgroup.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 10/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 18 presented below. In particular, whenthe encoder 110 performs LDPC encoding based on the parity check matrixdefined by Table 7, the group interleaver 122 may perform groupinterleaving by using π(j) defined as in Table 18 presented below:

TABLE 18 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 80 46 55 149 83 176 113 91 96 8 39 164 block of 21 12 9 71 44101 70 68 25 18 88 102 Group-wise 86 53 29 15 40 93 139 107 72 49 51 38interleaver 105 36 31 64 43 58 4 99 54 2 22 81 output, 106 90 11 37 1433 24 41 14 19 61 79 66 69 56 42 95 172 152 108 120 167 175 109 141 130179 116 115 151 162 171 169 155 146 158 170 119 148 174 144 129 131 137154 140 123 132 Order of bits group to be block interleaved π(j) (0 ≤ j< 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 3637 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 45 12752 7 161 47 178 27 57 97 114 block of 6 103 67 73 10 94 17 92 33 16 1Group-wise 30 76 74 48 34 5 82 126 85 78 23 interleaver 98 20 60 13 35104 32 65 135 50 84 output, 89 77 59 26 87 62 28 0 100 63 75 142 163 173168 110 153 150 166 138 117 125 122 177 136 134 112 157 145 118 160 121111 156 124 165 133 128 159 147

In the case of Table 18, Equation 16 may be expressed asX₀=Y_(π(0))=Y₈₀, X₁=Y_(π(1))=Y₄₆, X₂=Y_(π(2))=Y₅₅, . . . ,X₁₇₈=Y_(π(178))=Y₁₅₉, and X₁₇₉=Y_(π(179))=Y₁₄₇. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 0^(th) bit group to the 80^(th) bitgroup, the 1^(st) bit group to the 46^(th) bit group, the 2^(nd) bitgroup to the 55^(th) bit group, . . . , the 178^(th) bit group to the159^(th) bit group, and the 179^(th) bit group to the 147^(th) bitgroup.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 12/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 19 presented below.

TABLE 19 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 135 22 25 149 24 164 64 80 178 159 137 2 block of 11 157 79 7290 88 92 69 10 8 38 81 Group-wise 35 44 43 60 94 87 20 40 130 76 96 53interleaver 30 78 68 127 39 113 42 47 98 12 14 46 output, 41 129 71 17102 89 74 104 58 121 54 126 109 76 16 65 63 108 21 27 133 107 61 110 4895 124 15 101 111 177 179 165 145 163 112 153 140 166 128 120 131 146176 170 158 174 167 Order of bits group to be block interleaved π(j) (0≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 3536 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 6768 input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 29106 4 162 161 144 117 1 6 26 9 block of 66 123 75 28 59 5 114 119 132 7770 Group-wise 34 99 37 67 93 138 56 51 142 7 13 interleaver 32 33 55 8650 57 49 18 91 105 0 output, 143 103 3 139 62 97 45 31 36 134 82 100 84116 52 118 125 23 122 83 19 85 172 169 154 173 136 152 155 141 175 160151 150 147 168 171 156 115 148

In the case of Table 19, Equation 16 may be expressed asX₀=Y_(π(0))=Y₁₃₅, X₁=Y_(π(1))=Y₂₂, X₂=Y_(π(2))=Y₂₅, . . . ,X₁₇₈=Y_(π(178))=Y₁₁₅, and X₁₇₉=Y_(π(179))=Y₁₄₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 0^(th) bit group to the 135^(th) bitgroup, the 1^(st) bit group to the 22^(nd) bit group, the 2^(nd) bitgroup to the 25^(th) bit group, . . . , the 178^(th) bit group to the115^(th) bit group, and the 179^(th) bit group to the 148^(th) bitgroup.

In the above-described examples, the length of the LDPC codeword is64800 and the code rate is 6/15, 8/15, 10/15, and 12/15. However, thisis merely an example and the interleaving pattern may be definedvariously when the length of the LDPC codeword is 16200 or the code ratehas different values.

As described above, the group interleaver 122 may rearrange the order ofthe plurality of bit groups in bits group wise by using Equation 16 andTables 15 to 19.

“j-th block of Group-wise Interleaver input” in Tables 15 to 19indicates the j-th bit group input to the group interleaver 122 beforeinterleaving, and “π(j)-th block of Group-wise Interleaver output”indicates the π(j)-th bit group output from the group interleaver 122after interleaving.

In addition, since the order of the bit groups constituting the LDPCcodeword is rearranged by the group interleaver 122 in bits group wise,and then the bit groups are block-interleaved by the block interleaver124, which will be described below, “Order of bits groups to be blockinterleaved” is set forth in Tables 15 to 19 in relation to π(j).

π(j) defined as shown in Tables 15 to 19 may be arranged according tothe code rates as shown in Table 20:

TABLE 20 (CR 6/15) (CR 8/15) (CR 10/15) (CR 10/15) (CR 12/15) j-th blockof

 (j)-th block of

 (j)-th block of

 (j)-th block of

 (j)-th block of

 (j)-th block of Group-wise Group-wise Group-wise Group-wise Group-wiseGroup-wise Interleaver Interleaver Interleaver Interleaver InterleaverInterleaver input output output output output output 0 14 126 62 80 1351 35 50 4 46 22 2 24 38 94 55 25 3 96 36 164 149 149 4 44 66 29 83 24 5112 171 36 176 164 6 133 7 153 113 64 7 111 178 0 91 80 8 13 145 12 96178 9 57 67 19 8 159 10 136 49 38 39 137 11 118 137 101 164 2 12 7 16791 45 29 13 58 19 174 127 106 14 19 53 5 52 4 15 54 59 27 7 162 16 10168 162 161 161 17 42 52 156 47 144 18 43 23 140 178 117 19 41 42 171 271 20 114 78 83 57 6 21 1 97 95 97 26 22 36 102 64 114 9 23 16 96 72 2111 24 5 95 80 12 157 25 46 179 56 9 79 26 51 93 88 71 72 27 64 105 85 4490 28 70 92 53 101 88 29 49 77 9 70 92 30 40 73 47 68 69 31 37 107 12525 10 32 94 103 107 18 8 33 6 83 76 88 38 34 71 89 100 102 81 35 67 10074 6 66 36 50 28 65 103 123 37 55 64 103 67 75 38 39 24 79 73 28 39 3218 57 10 59 40 20 31 78 94 5 41 45 22 92 17 114 42 21 32 90 92 119 43 2560 126 33 132 44 47 71 26 16 77 45 59 94 70 1 70 46 60 70 16 86 35 47 1030 43 53 44 48 68 1 84 29 43 49 63 26 104 15 60 50 62 12 25 40 94 51 2 366 93 87 52 33 40 28 139 20 53 29 16 59 107 40 54 4 39 6 72 130 55 3 1567 49 76 56 23 35 106 51 96 57 15 4 8 38 53 58 27 51 1 30 34 59 18 88 376 99 60 66 62 15 74 37 61 31 14 96 48 67 62 22 90 99 34 93 63 9 45 81 5138 64 26 29 10 82 56 65 11 6 11 126 51 66 0 63 54 85 142 67 28 47 10278 7 68 30 56 87 23 13 69 34 5 115 105 30 70 8 34 98 36 78 71 17 8 23 3168 72 173 37 75 64 127 73 142 17 82 43 39 74 108 61 143 58 113 75 78 2141 4 42 76 74 33 49 99 47 77 65 0 33 54 98 78 97 43 58 2 12 79 149 20 7322 14 80 159 44 44 81 46 81 93 11 21 98 32 82 163 2 37 20 33 83 122 6963 60 55 84 150 10 122 13 86 85 137 57 68 35 50 86 99 48 69 104 57 87127 46 18 32 49 88 126 13 51 65 18 89 158 25 34 135 91 90 117 9 31 50105 91 154 55 42 84 0 92 86 65 35 106 41 93 128 27 20 90 129 94 130 5822 11 71 95 164 101 52 37 17 96 95 134 86 143 102 97 90 174 93 3 89 98100 99 77 24 74 99 177 159 45 41 104 100 120 166 30 14 58 101 80 81 1319 121 102 160 72 55 61 54 103 129 104 46 79 126 104 161 162 17 89 143105 76 79 48 77 103 106 72 146 24 59 3 107 98 130 50 26 139 108 85 150 287 62 109 174 127 40 62 97 110 169 76 89 28 45 111 104 153 32 0 31 112143 74 61 100 36 113 84 106 14 63 134 114 171 113 105 75 82 115 157 1637 66 109 116 178 176 39 69 73 117 82 131 97 56 16 118 151 111 60 42 65119 113 108 71 95 63 120 168 112 169 172 108 121 89 165 179 152 21 122141 75 170 108 27 123 179 121 128 120 133 124 88 124 155 167 107 125 14591 178 175 61 126 52 170 139 109 110 127 73 172 131 142 100 128 125 129120 163 84 129 139 140 141 173 116 130 79 120 130 168 52 131 75 86 158110 118 132 144 160 112 153 125 133 165 155 117 150 23 134 162 157 138166 122 135 87 164 127 138 83 136 48 85 147 117 19 137 134 84 142 125 85138 77 80 151 141 48 139 107 123 116 130 95 140 131 175 136 179 124 141138 154 176 116 15 142 109 161 167 115 101 143 92 152 154 151 111 144115 147 172 162 177 145 12 41 132 171 179 146 140 158 149 169 165 147153 132 145 155 145 148 56 138 144 146 163 149 91 114 108 158 112 150103 148 161 122 172 151 116 143 137 177 169 152 61 136 175 136 154 153172 125 150 134 173 154 167 173 118 112 136 155 123 116 165 157 152 156119 169 168 145 155 157 135 98 133 118 141 158 105 139 173 160 175 159124 115 111 121 160 160 155 118 119 111 151 161 38 119 152 170 153 162102 151 124 119 140 163 156 141 109 148 166 164 166 135 148 174 128 165132 177 160 144 120 166 110 87 177 129 131 167 81 128 146 131 146 168148 110 121 137 176 169 147 149 166 154 170 170 170 168 113 140 158 171175 144 123 123 174 172 106 122 163 132 167 173 83 109 110 156 150 174146 82 157 124 147 175 121 54 159 165 168 176 176 142 134 133 171 177 53133 135 128 156 178 69 156 129 159 115 179 152 117 114 147 148

Table 14 is the case in which group interleaving is performed usingEquation 15 and π(j) is applied as an index of an input bit group, andTable 20 is the case in which group interleaving is performed usingEquation 16 and π(j) is applied as an index of an output bit group.Therefore, Tables 14 and 20 have an inverse relationship with eachother.

The LDPC codeword which is group-interleaved in the above-describedmethod is illustrated in FIG. 6 . Comparing the LDPC codeword of FIG. 6and the LDPC codeword of FIG. 5 before group interleaving, it can beseen that the order of the plurality of bit groups constituting the LDPCcodeword is rearranged.

That is, as shown in FIGS. 5 and 6 , the groups of the LDPC codeword arearranged in order of bit group X₀, bit group X₁, . . . , bit groupX_(Ngroup−1) before being group-interleaved, and are arranged in anorder of bit group Y₀, bit group Y₁, . . . , bit group Y_(Ngroup−1)after being group-interleaved. In this case, the order of arranging thebit groups by the group interleaving may be determined based on Tables 9to 20.

The group twist interleaver 123 interleaves bits in a same group. Thatis, the group twist interleaver 123 may rearrange an order of bits in asame bit group by changing the order of the bits in the same bit group.

In this case, the group twist interleaver 123 may rearrange the order ofthe bits in the same bit group by cyclic-shifting a predetermined numberof bits from among the bits in the same bit group.

For example, as shown in FIG. 7 , the group twist interleaver 123 maycyclic-shift bits included in the bit group Y₁ to the right by 1 bit. Inthis case, the bits located in the 0^(th) position, the 1^(st) position,the 2^(nd) position, . . . , the 358^(th) position, and the 359^(th)position in the bit group Y₁ as shown in FIG. 7 are cyclic-shifted tothe right by 1 bit. As a result, the bit located in the 359^(th)position before being cyclic-shifted is located in the front of the bitgroup Y₁ and the bits located in the 0^(th) position, the 1^(st)position, the 2^(nd) position, . . . , the 358^(th) position beforebeing cyclic-shifted are shifted to the right serially by 1 bit andlocated.

In addition, the group twist interleaver 123 may rearrange the order ofbits in each bit group by cyclic-shifting a different number of bits ineach bit group.

For example, the group twist interleaver 123 may cyclic-shift the bitsincluded in the bit group Y₁ to the right by 1 bit, and may cyclic-shiftthe bits included in the bit group Y₂ to the right by 3 bits.

However, the group twist interleaver 123 may be omitted according tocircumstances.

In addition, the group twist interleaver 123 is placed after the groupinterleaver 122 in the above-described example. However, this is merelyan example. That is, the group twist interleaver 123 changes only theorder of bits in a certain bit group and does not change the order ofthe bit groups. Therefore, the group twist interleaver 123 may be placedbefore the group interleaver 122.

The block interleaver 124 interleaves the plurality of bit groups theorder of which has been rearranged. Specifically, the block interleaver124 may interleave the plurality of bit groups the order of which hasbeen rearranged by the group interleaver 122 in bits group wise (orgroup units). The block interleaver 124 is formed of a plurality ofcolumns each including a plurality of rows, and may interleave bydividing the plurality of rearranged bit groups based on a modulationorder determined according to a modulation method.

In this case, the block interleaver 124 may interleave the plurality ofbit groups the order of which has been rearranged by the groupinterleaver 122 in bits group wise. Specifically, the block interleaver124 may interleave by dividing the plurality of rearranged bit groupsaccording to a modulation order by using a first part and a second part.

Specifically, the block interleaver 124 interleaves by dividing each ofthe plurality of columns into a first part and a second part, writingthe plurality of bit groups in the plurality of columns of the firstpart serially in bits group wise, dividing bits of the other bit groupsinto groups (or sub bit groups) each including a predetermined number ofbits based on the number of columns, and writing the sub bit groups inthe plurality of columns of the second part serially.

Here, the number of bit groups which are interleaved in bits group wisemay be determined by at least one of the number of rows and columnsconstituting the block interleaver 124, the number of bit groups, andthe number of bits included in each bit group. In other words, the blockinterleaver 124 may determine bit groups which are to be interleaved inbits group wise considering at least one of the number of rows andcolumns constituting the block interleaver 124, the number of bitgroups, and the number of bits included in each bit group, interleavethe corresponding bit groups in bits group wise, and divide bits of theother bit groups into sub bit groups and interleave the sub bit groups.For example, the block interleaver 124 may interleave at least part ofthe plurality of bit groups in bits group wise using the first part, anddivide bits of the other bit groups into sub bit groups and interleavethe sub bit groups using the second part.

Meanwhile, interleaving bit groups in bits group wise (or in bit groupunits) means that bits included in a same bit group are written in asame column. In other words, the block interleaver 124, in case of bitgroups which are interleaved in bits group wise, may not divide the bitsincluded in the same bit groups and instead write the bits in the samecolumn. However, in case of bit groups which are not interleaved in bitsgroup wise, may divide bits in at least one of these bit groups or eachof these bit groups and write the bits in different columns.

Accordingly, the number of rows constituting the first part is aninteger multiple of the number of bits included in one bit group (forexample, 360), and the number of rows constituting the second part maybe less than the number of bits included in this bit group.

In addition, in all bit groups interleaved by the first part, bitsincluded in a same bit group are written and interleaved in a samecolumn of the first part, and in at least one group interleaved by thesecond part, bits are divided and written in at least two columns of thesecond part.

The interleaving method will be described later.

Meanwhile, the group twist interleaver 123 changes only an order of bitsin a bit group and does not change the order of bit groups byinterleaving. Accordingly, an order of bit groups to beblock-interleaved by the block interleaver 124, that is, the order ofthe bit groups to be input to the block interleaver 124, may bedetermined by the group interleaver 122. For example, the order of thebit groups to be block-interleaved by the block interleaver 124 may bedetermined by π(j) defined in Tables 9 to 20.

As described above, the block interleaver 124 may interleave theplurality of bit groups the order of which has been rearranged in bitsgroup wise by using the plurality of columns each including theplurality of rows.

In this case, the block interleaver 124 may interleave the LDPC codewordby dividing the plurality of columns into at least two parts. Forexample, the block interleaver 124 may divide each of the plurality ofcolumns into the first part and the second part and interleave theplurality of bit groups constituting the LDPC codeword.

In this case, the block interleaver 124 may divide each of the pluralityof columns into N number of parts (N is an integer greater than or equalto 2) according to whether the number of bit groups constituting theLDPC codeword is an integer multiple of the number of columnsconstituting the block interleaver 124, and may perform interleaving.

When the number of bit groups constituting the LDPC codeword is aninteger multiple of the number of columns constituting the blockinterleaver 124, the block interleaver 124 may interleave the pluralityof bit groups constituting the LDPC codeword in bits group wise withoutdividing each of the plurality of columns into parts.

Specifically, the block interleaver 124 may interleave by writing theplurality of bit groups of the LDPC codeword on each of the columns inbits group wise in a column direction, and reading each row of theplurality of columns in which the plurality of bit groups are written inbits group wise in a row direction.

In this case, the block interleaver 124 may interleave by writing bitsincluded in a predetermined number of bit groups, which corresponds to aquotient obtained by dividing the number of bit groups of the LDPCcodeword by the number of columns of the block interleaver 124, on eachof the plurality of columns serially in a column direction, and readingeach row of the plurality of columns in which the bits are written in arow direction.

Hereinafter, the bit group located in the j^(th) position after beinginterleaved by the group interleaver 122 will be referred to as groupY_(j).

For example, it is assumed that the block interleaver 124 is formed of Cnumber of columns each including R₁ number of rows. In addition, it isassumed that the LDPC codeword is formed of N_(group) number of bitgroups and the number of bit groups N_(group) is an integer multiple ofC.

In this case, when the quotient obtained by dividing N_(group) number ofbit groups constituting the LDPC codeword by C number of columnsconstituting the block interleaver 124 is A (=N_(group)/C) (A is aninteger greater than 0), the block interleaver 124 may interleave bywriting A (=N_(group)/C) number of bit groups on each column serially inthe column direction and reading bits written on each column in the rowdirection.

For example, as shown in FIG. 8 , the block interleaver 124 writes bitsincluded in bit group Y₀, bit group Y₁, . . . , bit group Y_(A−1) in the1^(st) column from the 1^(st) row to the R₁ ^(th) row, writes bitsincluded in bit group Y_(A), bit group Y_(A+1), . . . , bit groupY_(2A−1) in the 2nd column from the 1^(st) row to the R₁ ^(th) row, . .. , and writes bits included in bit group Y_(CA−A), bit groupY_(CA−A+1), bit group Y_(CA−1) in the column C from the 1^(st) row tothe R₁ ^(th) row. The block interleaver 124 may read the bits written ineach row of the plurality of columns in the row direction.

Accordingly, the block interleaver 124 interleaves all bit groupsconstituting the LDPC codeword in bits group wise.

However, when the number of bit groups of the LDPC codeword is not aninteger multiple of the number of columns of the block interleaver 124,the block interleaver 124 may divide each column into two parts andinterleave a part of the plurality of bit groups of the LDPC codeword inbits group wise, and divide bits of the other bit groups into sub bitgroups and interleave the sub bit groups. In this case, the bitsincluded in the other bit groups, that is, the bits included in thenumber of groups which correspond to the remainder when the number ofbit groups constituting the LDPC codeword is divided by the number ofcolumns are not interleaved in bits group wise, but interleaved by beingdivided according to the number of columns.

Specifically, the block interleaver 124 may interleave the LDPC codewordby dividing each of the plurality of columns into two parts.

In this case, the block interleaver 124 may divide the plurality ofcolumns into the first part and the second part based on at least one ofthe number of rows and columns of the block interleaver 124, the numberof bit groups constituting the LDPC codeword, and the number of bitsconstituting each of the bit groups.

Here, each of the plurality of bit groups may be formed of 360 bits. Inaddition, the number of bit groups of the LDPC codeword is determinedbased on the length of the LDPC codeword and the number of bits includedin each bit group. For example, when an LDPC codeword in the length of16200 is divided such that each bit group has 360 bits, the LDPCcodeword is divided into 45 bit groups. Alternatively, when an LDPCcodeword in the length of 64800 is divided such that each bit group has360 bits, the LDPC codeword may be divided into 180 bit groups. Further,the number of columns constituting the block interleaver 124 may bedetermined according to a modulation method. This will be explained indetail below.

Accordingly, the number of rows constituting each of the first part andthe second part may be determined based on the number of columnsconstituting the block interleaver 124, the number of bit groupsconstituting the LDPC codeword, and the number of bits constituting eachof the plurality of bit groups.

Specifically, in each of the plurality of columns, the first part may beformed of as many rows as the number of bits constituting at least onebit group, which can be written in each column in bits group wise, fromamong the plurality of bit groups of the LDPC codeword, according to thenumber of columns constituting the block interleaver 124, the number ofbit groups constituting the LDPC codeword, and the number of bitsconstituting each bit group.

In each of the plurality of columns, the second part may be formed ofrows excluding as many rows as the number of bits constituting at leastsome bit groups, which can be written in each of the plurality ofcolumns in bits group wise, from among the plurality of bit groups ofthe LDPC codeword. Specifically, the number rows of the second part maybe the same value as a quotient when the number of bits included in allbit groups excluding bit groups corresponding to the first part isdivided by the number of columns constituting the block interleaver 124.In other words, the number of rows of the second part may be the samevalue as a quotient when the number of bits included in the remainingbit groups which are not written in the first part from among bit groupsconstituting the LDPC codeword is divided by the number of columns.

That is, the block interleaver 124 may divide each of the plurality ofcolumns into the first part including as many rows as the number of bitsincluded in bit groups which can be written in each column in bits groupwise, and the second part including the other rows.

Accordingly, the first part may be formed of as many rows as the numberof bits included in bit groups, that is, as many rows as an integermultiple of M. However, since the number of codeword bits constitutingeach bit group may be an aliquot part of M as described above, the firstpart may be formed of as many rows as an integer multiple of the numberof bits constituting each bit group.

In this case, the block interleaver 124 may interleave by writing andreading the LDPC codeword in the first part and the second part in thesame method.

Specifically, the block interleaver 124 may interleave by writing theLDPC codeword in the plurality of columns constituting each of the firstpart and the second part in a column direction, and reading theplurality of columns constituting the first part and the second part inwhich the LDPC codeword is written in a row direction.

That is, the block interleaver 124 may interleave by writing the bitsincluded in at least some bit groups, which can be written in each ofthe plurality of columns in bits group wise among the plurality of bitgroups constituting the LDPC codeword, in each of the plurality ofcolumns of the first part serially, dividing the bits included in theother bit groups and writing these divided bits in the plurality ofcolumns of the second part in the column direction, and reading the bitswritten in each of the plurality of columns constituting each of thefirst part and the second part in the row direction.

In this case, the block interleaver 124 may interleave by dividing theother bit groups from among the plurality of bit groups constituting theLDPC codeword based on the number of columns constituting the blockinterleaver 124.

Specifically, the block interleaver 124 may interleave by dividing thebits included in the other bit groups by the number of a plurality ofcolumns, writing each of the divided bits in each of the plurality ofcolumns constituting the second part in the column direction, andreading the plurality of columns constituting the second part, where thedivided bits are written, in the row direction.

That is, the block interleaver 124 may divide the bits included in theother bit groups among the plurality of bit groups of the LDPC codeword,that is, the bits in the number of bit groups which correspond to theremainder when the number of bit groups constituting the LDPC codewordis divided by the number of columns, by the number of columns, and maywrite the divided bits in each column of the second part serially in thecolumn direction.

For example, it is assumed that the block interleaver 124 is formed of Cnumber of columns each including R₁ number of rows. In addition, it isassumed that the LDPC codeword is formed of N_(group) number of bitgroups, the number of bit groups N_(group) is not an integer multiple ofC, and A×C+1=N_(group) (A is an integer greater than 0). In other words,it is assumed that when the number of bit groups constituting the LDPCcodeword is divided by the number of columns, the quotient is A and theremainder is 1.

In this case, as shown in FIGS. 9 and 10 , the block interleaver 124 maydivide each column into a first part including R₁ number of rows and asecond part including R₂ number of rows. In this case, R₁ may correspondto the number of bits included in bit groups which can be written ineach column in bits group wise, and R₂ may be R₁ subtracted from thenumber of rows of each column.

That is, in the above-described example, the number of bit groups whichcan be written in each column in bits group wise is A, and the firstpart of each column may be formed of as many rows as the number of bitsincluded in A number of bit groups, that is, may be formed of as manyrows as A×M number.

In this case, the block interleaver 124 writes the bits included in thebit groups which can be written in each column in bits group wise, thatis, A number of bit groups, in the first part of each column in thecolumn direction.

That is, as shown in FIGS. 9 and 10 , the block interleaver 124 writesthe bits included in each of bit group Y₀, bit group Y₁, . . . , groupY_(A−1) in the 1^(st) to R₁ ^(th) rows of the first part of the 1^(st)column, writes bits included in each of bit group Y_(A), bit groupY_(A+1), . . . , bit group Y_(2A−1) in the 1^(st) to R₁ ^(th) rows ofthe first part of the 2^(nd) column, . . . , writes bits included ineach of bit group Y_(CA−A), bit group Y_(CA−A+1), . . . , bit groupY_(CA−1) in the 1^(st) to R₁ ^(th) rows of the first part of the columnC.

As described above, the block interleaver 124 writes the bits includedin the bit groups which can be written in each column in bits group wisein the first part of each column in bits group wise.

In other words, in the above exemplary embodiment, the bits included ineach of bit group (Y₀), bit group (Y₁), . . . , bit group (Y_(A−1)) maynot be divided and all of the bits may be written in the first column,the bits included in each of bit group (Y_(A)), bit group (Y_(A+1)), . .. , bit group (Y_(2A−1)) may not be divided and all of the bits may bewritten in the second column, . . . , and the bits included in each ofbit group (Y_(CA−A)), bit group (Y_(CA−A+1)), . . . , group (Y_(CA−1))may not be divided and all of the bits may be written in the C column.As such, bits included in a same bit group in all bit groups interleavedby the first part are written in a same column of the first part.

Thereafter, the block interleaver 124 divides the bits included in thegroups other than the bit groups written in the first part of eachcolumn from among the plurality of bit groups, and writes these bits inthe second part of each column in the column direction. In this case,the block interleaver 124 divides the bits included in the other bitgroups such that a same number of bits are written in the second part ofeach column in the column direction. Here, an order of writing bits inthe first part and the second part may be reversed. That is, bits may bewritten in the second part ahead of the first part according to anexemplary embodiment.

In the above-described example, since A×C+1=N_(group) when the bitgroups constituting the LDPC codeword are written in the first partserially, the last bit group Y_(Ngroup−1) of the LDPC codeword is notwritten in the first part and remains. Accordingly, the blockinterleaver 124 divides the bits included in the bit group Y_(Ngroup−1)into C number of sub bit groups as shown in FIG. 9 , and writes thedivided bits (that is, the bits corresponding to the quotient when thebits included in the last group (Y_(Ngroup−1)) are divided by C) in thesecond part of each column serially.

The bits divided based on the number of columns may be referred to assub bit groups. In this case, each of the sub bit groups may be writtenin each column of the second part. That is, the bits included in the bitgroups may be divided and may form the sub bit groups.

That is, the block interleaver 124 writes the bits in the 1^(st) to R₂^(th) rows of the second part of the 1^(st) column, writes the bits inthe 1^(st) to R₂ ^(th) rows of the second part of the 2^(nd) column, . .. , and writes the bits in the 1^(st) to R₂ ^(th) rows of the secondpart of the column C. In this case, the block interleaver 124 may writethe bits in the second part of each column in the column direction asshown in FIG. 9 .

That is, in the second part, bits constituting a bit group may not bewritten in a same column and may be written in a plurality of columns.In other words, in the above example, the last bit group (Y_(Ngroup−1))is formed of M number of bits and thus, the bits included in the lastbit group (Y_(Ngroup−1)) may be divided by M/C and written in eachcolumn. That is, the bits included in the last bit group (Y_(Ngroup−1))are divided by M/C, forming M/C number of sub bit groups, and each ofthe sub bit groups may be written in each column of the second part.

Accordingly, in at least one bit group which is interleaved by thesecond part, the bits included in the at least one bit group are dividedand written in at least two columns constituting the second part.

In the above-described example, the block interleaver 124 writes thebits in the second part in the column direction. However, this is merelyan example. That is, the block interleaver 124 may write the bits in theplurality of columns of the second parts in the row direction. In thiscase, the block interleaver 124 may write the bits in the first part inthe same method as described above.

Specifically, referring to FIG. 10 , the block interleaver 124 writesthe bits from the 1^(st) row of the second part in the 1^(st) column tothe 1^(st) row of the second part in the column C, writes the bits fromthe 2^(nd) row of the second part in the 1^(st) column to the 2^(nd) rowof the second part in the column C, . . . , and writes the bits from theR₂ ^(th) row of the second part in the column to the R₂ ^(th) row of thesecond part in the column C.

On the other hand, the block interleaver 124 reads the bits written ineach row of each part serially in the row direction. That is, as shownin FIGS. 9 and 10 , the block interleaver 124 reads the bits written ineach row of the first part of the plurality of columns serially in therow direction, and reads the bits written in each row of the second partof the plurality of columns serially in the row direction.

Accordingly, the block interleaver 124 may interleave a part of theplurality of bit groups constituting the LDPC codeword in bits groupwise, and divide and interleave some of the remaining bit groups. Thatis, the block interleaver 124 may interleave by writing the LDPCcodeword constituting a predetermined number of bit groups from amongthe plurality of bit groups in the plurality of columns of the firstpart in bits group wise, dividing the bits of the other bit groups andwriting the bits in each of the columns of the second part, and readingthe plurality of columns of the first and second parts in the rowdirection.

As described above, the block interleaver 124 may interleave theplurality of bit groups in the methods described above with reference toFIGS. 8 to 10 .

In particular, in the case of FIG. 9 , the bits included in the bitgroup which does not belong to the first part are written in the secondpart in the column direction and read in the row direction. In view ofthis, the order of the bits included in the bit group which does notbelong to the first part is rearranged. Since the bits included in thebit group which does not belong to the first part are interleaved asdescribed above, Bit Error Rate (BER)/Frame Error Rate (FER) performancecan be improved in comparison with a case in which such bits are notinterleaved.

However, the bit group which does not belong to the first part may notbe interleaved as shown in FIG. 10 . That is, since the blockinterleaver 124 writes and read the bits included in the bit group whichdoes not belong to the first part in and from the second part in the rowdirection, the order of the bits included in the bit group which doesnot belong to the first part is not changed and these bits are output tothe modulator 130 serially. In this case, the bits included in the bitgroup which does not belong to the first part may be output serially tobe mapped onto a modulation symbol.

In FIGS. 9 and 10 , the last single bit group of the plurality of bitgroups is written in the second part. However, this is merely anexample. The number of bit groups written in the second part may varyaccording to the number of bit groups constituting the LDPC codeword,the number of bits constituting each of the bit groups, the number ofcolumns and rows of the block interleaver, the number of transmissionantennas, etc.

The block interleaver 124 may have a configuration as shown in Tables 21and 22 presented below:

TABLE 21 N_(lpdc) = 64800 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C2 4 6 8 10 12 R₁ 32400 16200 10800 7920 6480 5400 R₂ 0 0 0 180 0 0

TABLE 22 N_(ldpc) = 16200 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C2 4 6 8 10 12 R₁ 7920 3960 2520 1800 1440 1080 R₂ 180 90 180 225 180 270

Herein, C (or N_(C)) is the number of columns of the block interleaver124, R₁ is the number of rows constituting the first part in eachcolumn, and R₂ is the number of rows constituting the second part ineach column.

Referring to Tables 21 and 22, C is the same value as a modulation orderaccording to a modulation method, and each of a plurality of columns isformed of rows corresponding to a value obtained by dividing the numberof bits constituting the LDPC codeword by the number of a plurality ofcolumns.

For example, when the length N_(lpdc) of the LDPC codeword is 64800 andthe modulation method is 1024-QAM, the block interleaver 124 is formedof 10 columns as the modulation order is 10 in the case of 1024-QAM, andeach column is formed of as many rows as R₁+R₂=6480(=64800/10).

Meanwhile, referring to Tables 21 and 22, when the number of bit groupsconstituting the LDPC codeword is an integer multiple of the number ofcolumns, the block interleaver 124 interleaves without dividing eachcolumn. Therefore, R₁ corresponds to the number of rows constitutingeach column, and R₂ is 0. In addition, when the number of bit groupsconstituting the LDPC codeword is not an integer multiple of the numberof columns, the block interleaver 124 interleaves the groups by dividingeach column into the first part formed of R₁ number of rows, and thesecond part formed of R₂ number of rows.

When the number of columns of the block interleaver 124 is equal to thenumber of bits constituting a modulation symbol as shown in Tables 21and 22, bits included in a same bit group are mapped onto a single bitof each modulation symbol.

For example, when N_(ldpc)=64800 and the modulation method is 1024-QAM,the block interleaver 124 may be formed of 10 columns each including6480 rows. In this case, the bits included in each of the plurality ofbit groups are written in the 10 columns and bits written in the samerow in each column are output serially. In this case, since 10 bitsconstitute a single modulation symbol in the modulation method of1024-QAM, bits included in the same bit group, that is, bits output froma single column, may be mapped onto a single bit of each modulationsymbol. For example, bits included in a bit group written in the 1^(st)column may be mapped onto a first bit of each modulation symbol.

Referring to Tables 21 and 22, the total number of rows of the blockinterleaver 124, that is, R₁+R₂, is N_(ldpc)/C.

In addition, the number of rows of the first part, R₁, is an integermultiple of the number of bits included in each group, M (e.g., M=360),and maybe expressed as └N_(group)/C┘×M, and the number of rows of thesecond part, R₂, may be N_(ldpc)/C−R₁. Herein, └N_(group)/C┘ is thelargest integer below N_(group)/C. Since R₁ is an integer multiple ofthe number of bits included in each group, M, bits may be written in R₁in bit groups wise.

In addition, when the number of bit groups of the LDPC codeword is notan integer multiple of the number of columns, it can be seen from Tables21 and 22 that the block interleaver 124 interleaves by dividing eachcolumn into two parts.

Specifically, the length of the LDPC codeword divided by the number ofcolumns is the total number of rows included in the each column. In thiscase, when the number of bit groups of the LDPC codeword is an integermultiple of the number of columns, each column is not divided into twoparts. However, when the number of bit groups of the LDPC codeword isnot an integer multiple of the number of columns, each column is dividedinto two parts.

For example, it is assumed that the number of columns of the blockinterleaver 124 is identical to the number of bits constituting amodulation symbol, and an LDPC codeword is formed of 64800 bits as shownin Table 21. In this case, each bit group of the LDPC codeword is formedof 360 bits, and the LDPC codeword is formed of 64800/360 (=180) bitgroups.

When the modulation method is 1024-QAM, the block interleaver 124 may beformed of 10 columns and each column may have 64800/10 (=6480) rows.

In this case, since the number of bit groups of the LDPC codeworddivided by the number of columns is 180/10 (=18), bits can be written ineach column in bits group wise without dividing each column into twoparts. That is, bits included in 18 bit groups which is the quotientwhen the number of bit groups constituting the LDPC codeword is dividedby the number of columns, that is, 18×360 (=6480) bits can be written ineach column.

However, when the modulation method is 256-QAM, the block interleaver124 may be formed of eight (8) columns and each column may have 64800/8(=8100) rows.

In this case, since the number of bit groups of the LDPC codeworddivided by the number of columns is 180/8=22.5, the number of bit groupsconstituting the LDPC codeword is not an integer multiple of the numberof columns. Accordingly, the block interleaver 124 divides each of theeight (8) columns into two parts to perform interleaving in bits groupwise.

In this case, since the bits should be written in the first part of eachcolumn in bits group wise, the number of bit groups which can be writtenin the first part of each column in bits group wise is 22 which is thequotient when the number of bit groups constituting the LDPC codeword isdivided by the number of columns, and accordingly, the first part ofeach column has 22×360 (=7920) rows. Accordingly, 7920 bits included in22 bit groups may be written in the first part of each column.

The second part of each column has rows which are the rows of the firstpart subtracted from the total rows of each column. Accordingly, thesecond part of each column includes 8100-7920 (=180) rows.

In this case, bits included in the other bit groups which have not beenwritten in the first part are divided and written in the second part ofeach column.

Specifically, since 22×8 (=176) bit groups are written in the firstpart, the number of bit groups to be written in the second part is180-176 (=4) (for example, a bit group Y₁₇₆, bit group Y₁₇₇, bit groupY₁₇₈, and bit group Y₁₇₉ from among bit group Y₀, bit group Y₁, bitgroup Y₂, . . . , bit group Y₁₇₈, and bit group Y₁₇₉ constituting theLDPC codeword).

Accordingly, the block interleaver 124 may write the four (4) bit groupswhich have not been written in the first part and remains from among thebit groups constituting the LDPC codeword in the second part of eachcolumn serially.

That is, the block interleaver 124 may write 180 bits of the 360 bitsincluded in the bit group Y₁₇₆ in the 1^(st) row to the 180^(th) row ofthe second part of the 1^(st) column in the column direction, and maywrite the other 180 bits in the 1^(st) row to the 180^(th) row of thesecond part of the 2^(nd) column in the column direction. In addition,the block interleaver 124 may write 180 bits of the 360 bits included inthe bit group Y₁₇₇ in the 1^(st) row to the 180^(th) row of the secondpart of the 3^(rd) column in the column direction, and may write theother 180 bits in the 1^(st) row to the 180^(th) row of the second partof the 4^(th) column in the column direction. In addition, the blockinterleaver 124 may write 180 bits of the 360 bits included in the bitgroup Y₁₇₈ in the 1^(st) row to the 180^(th) row of the second part ofthe 5^(th) column in the column direction, and may write the other 180bits in the 1^(st) row to the 180^(th) row of the second part of the6^(th) column in the column direction. In addition, the blockinterleaver 124 may write 180 bits of the 360 bits included in the bitgroup Y₁₇₉ in the 1^(st) row to the 180^(th) row of the second part ofthe 7^(th) column in the column direction, and may write the other 180bits in the 1^(st) row to the 180^(th) row of the second part of the8^(th) column in the column direction.

Accordingly, bits included in a bit group which has not been written inthe first part and remains are not written in a same column in thesecond part and may be divided and written in a plurality of columns.

Hereinafter, the block interleaver 124 of FIG. 4 according to anexemplary embodiment will be explained in detail with reference to FIG.11 .

In a group-interleaved LDPC codeword (v₀, v₁, . . . , v_(N) _(ldpc) ⁻¹),Y_(j) is continuously arranged like V={Y₀, Y₁, . . . , Y_(N) _(ldpc)⁻¹}.

The LDPC codeword after group interleaving may be interleaved by theblock interleaver 124 as shown in FIG. 11 . In this case, the blockinterleaver 124 divides a plurality of columns into the first part(Part 1) and the second part (Part 2) based on the number of columns ofthe block interleaver 124 and the number of bits of a bit group. In thiscase, in the first part, bits constituting a bit group may be written ina same column, and in the second part, bits constituting a bit group maybe written in a plurality of columns (i.e. bits constituting a bit groupmay be written in at least two columns).

Specifically, input bits v_(i) are written serially from the first partto the second part column wise, and then read out serially from thefirst part to the second part row wise. That is, the data bits v_(i) arewritten serially into the block interleaver column-wise starting in thefirst part and continuing column-wise finishing in the second part, andthen read out serially row-wise from the first part and then row-wisefrom the second part. Accordingly, each bit included in a same bit groupin the first part may be mapped onto a single bit of each modulationsymbol.

In this case, the number of columns and the number of rows of the firstpart and the second part of the block interleaver 124 vary according toa modulation format and a length of the LDPC codeword as in Table 23presented below. That is, the first part and the second part blockinterleaving configurations for each modulation format and code lengthare specified in Table 23 presented below. Herein, the number of columnsof the block interleaver 124 may be equal to the number of bitsconstituting a modulation symbol. In addition, a sum of the number ofrows of the first part, N_(r1) and the number of rows of the secondpart, N_(r2), is equal to N_(ldpc)/N_(C) (herein, N_(C) is the number ofcolumns). In addition, since N_(r1)(=└N_(group)/N_(c)┘×360) is amultiple of 360, a multiple of bits groups may be written in the firstpart.

TABLE 23 Rows in Part 1 N_(r1) Rows in Part 2 N_(r2) N_(ldpc) = N_(ldpc)= N_(ldpc) = N_(ldpc) = Columns Modulation 64800 16200 64800 16200 N_(c)QPSK 32400 7920 0 180 2  16-QAM 16200 3960 0 90 4  64-QAM 10800 2520 0180 6  256-QAM 7920 1800 180 225 8 1024-QAM 6480 1440 0 180 10 4096-QAM5400 1080 0 270 12

Hereinafter, an operation of the block interleaver 124 will be explainedin detail.

Specifically, as shown in FIG. 11 , the input bit v_(i)(0≤i<N_(C)×N_(r1)) is written in an r_(i) row of a c_(i) column of thefirst part of the block interleaver 124. Herein, c_(i) and r_(i) are

$c_{i} = \left\lfloor \frac{i}{N_{r1}} \right\rfloor$and r_(i)=(i mod N_(r1)), respectively.

In addition, the input bit v_(i) (N_(C)×N_(r1)≤i<N_(ldpc)) is written inan r_(i) row of c_(i) column of the second part of the block interleaver124. Herein, c_(i) and r_(i) satisfy

$c_{i} = \left\lfloor \frac{\left( {i - {N_{C} \times N_{r1}}} \right)}{N_{r2}} \right\rfloor$and r_(i)=N_(r1)+{(i−N_(C)×N_(r1))mod N_(r2)}, respectively.

An output bit q_(j) (0≤j<N_(ldpc)) is read from a c_(j) column of anr_(j) row. Herein, r_(j) and c_(j) satisfy

$r_{j} = \left\lfloor \frac{j}{N_{c}} \right\rfloor$and c_(j)=(j mod N_(C)), respectively.

For example, when the length N_(ldpc) of the LDPC codeword is 64800 andthe modulation method is 256-QAM, the order of bits output from theblock interleaver 124 may be (q₀, q₁, q₂, . . . , q₆₃₃₅₇, q₆₃₃₅₈,q₆₃₃₅₉, q₆₃₃₆₀, q₆₃₃₆₁, . . . , q₆₄₇₉₉)=(v₀, v₇₉₂₀, v₁₅₈₄₀, . . .v₄₇₅₁₉, v₅₅₄₃₉, v₆₃₃₅₉, v₆₃₃₆₀, v₆₃₅₄₀, . . . , v₆₄₇₉₉). Here, theindexes of the right side of the foregoing equation may be specificallyexpressed for the eight (8) columns as 0, 7920, 15840, 23760, 31680,39600, 47520, 55440, 1, 7921, 15841, 23761, 31681, 39601, 47521, 55441,. . . , 7919, 15839, 23759, 31679, 39599, 47519, 55439, 63359, 63360,63540, 63720, 63900, 64080, 64260, 64440, 64620, . . . , 63539, 63719,63899, 64079, 64259, 64439, 64619, 64799.

Hereinafter, an interleaving operation of the block interleaver 124 willbe explained in detail.

The block interleaver 124 may interleave by writing a plurality of bitgroups in each column in bits group wise in the column direction, andreading each row of the plurality of columns in which the plurality ofbit groups are written in bits group wise in the row direction.

In this case, the number of columns constituting the block interleaver124 may vary according to a modulation method, and the number of rowsmay be the length of the LDPC codeword divided by the number of columns.

For example, when the modulation method is 1024-QAM, the blockinterleaver 124 may be formed of 10 columns. In this case, when thelength N_(ldpc) of the LDPC codeword is 64800, the number of rows is6480 (=64800/10).

Hereinafter, a method for interleaving the plurality of bit groups inbits group wise by the block interleaver 124 will be explained indetail.

When the number of bit groups constituting the LDPC codeword is aninteger multiple of the number of columns, the block interleaver 124 mayinterleave by writing the bit groups as many as the number of bit groupsdivided by the number of columns in each column serially in bits groupwise.

For example, when the modulation method is 1024-QAM and the lengthN_(ldpc) of the LDPC codeword is 64800, the block interleaver 124 may beformed of 10 columns each including 6480 rows. In this case, since theLDPC codeword is divided into (64800/360=180) number of bit groups whenthe length N_(ldpc) of the LDPC codeword is 64800, the number of bitgroups (=180) of the LDPC codeword may be an integer multiple of thenumber of columns (=10) when the modulation method is 1024-QAM. That is,no remainder is generated when the number of bit groups of the LDPCcodeword is divided by the number of columns.

As described above, when the number of bit groups of the LDPC codewordis an integer multiple of the number of columns of the block interleaver124, the block interleaver 124 may not divide each column into parts andmay interleave by writing, in each of the plurality of columns seriallyin the column direction, the bits included in the bit groups whichcorrespond to the quotient when the number of bits groups of the LDPCcodeword is divided by the number of columns of the block interleaver124, and reading each row of the plurality of columns in which the bitsare written in the row direction.

For example, as shown in FIG. 12 , the block interleaver 124 writes bitsincluded in each of bit group Y₀, bit group Y₁, . . . , bit group Y₁₇ inthe 1^(st) row to 6480^(th) row of the first column, writes bitsincluded in each of bit group Y₁₈, bit group Y₁₉, . . . , bit group Y₃₅in the 1st row to 6480^(th) row of the second column, . . . , and writesthe bits included in each of bit group Y₁₆₂, bit group Y₁₆₃, . . . , bitgroup Y₁₇₉ in the 1^(st) row to 6480^(th) row of the 10^(th) column. Inaddition, the block interleaver 124 may read the bits written in eachrow of the 10 columns serially in the row direction.

As described above, when the number of bit groups constituting an LDPCcodeword is an integer multiple of the number of columns of the blockinterleaver 124, the block interleaver 124 may interleave the pluralityof bit groups in bits group wise, and accordingly, bits belonging to asame bit group may be written in a same column.

As described above, the block interleaver 124 may interleave theplurality of bit groups of the LDPC codeword in the methods describedabove with reference to FIGS. 8 to 12 .

When the number of columns constituting the block interleaver 124 hasthe same value as the modulation degree as in the above-describedexample, bits included in a same bit group may be mapped onto a singlebit of each modulation symbol.

However, this is merely an example and bits included in a same bit groupmay be mapped onto two bits of each modulation symbol. In this case, theblock interleaver 124 may have a configuration as shown in Tables 24 and25 presented below. In this case, the number of columns constituting theblock interleaver 124 may be a half of the modulation order as shown inTables 24 and 25.

TABLE 24 N_(ldpc) = 64800 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C1 2 3 4 5 6 R₁ 64800 32400 21600 16200 12960 10800 R₂ 0 0 0 0 0 0

TABLE 25 N_(ldpc) = 16200 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C1 2 3 4 5 6 R₁ 16200 7920 5400 3960 3240 2520 R₂ 0 180 0 90 0 180

Herein, C (or N_(C)) is the number of columns of the block interleaver124, R₁ is the number of rows constituting the first part in eachcolumn, and R₂ is the number of rows constituting the second part ineach column.

Referring to Tables 24 and 25, when the number of bit groupsconstituting an LDPC codeword is an integer multiple of the number ofcolumns, the block interleaver 124 interleaves without dividing eachcolumn. Therefore, R₁ corresponds to the number of rows constitutingeach column, and R₂ is 0. In addition, when the number of bit groupsconstituting the LDPC codeword is not an integer multiple of the numberof columns, the block interleaver 124 interleaves the bit groups bydividing each column into the first part formed of R₁ number of rows,and the second part formed of R₂ number of rows.

When the number of columns of the block interleaver 124 is a half of thenumber of bits constituting the modulation symbol as shown in Tables 24and 25, bits included in a same bit group may be mapped onto two bits ofeach modulation symbol.

For example, when N_(ldpc)=64800 and the modulation method is 1024-QAM,the block interleaver 124 may be formed of five (5) columns eachincluding 12960 rows. In this case, a plurality of bit groupsconstituting an LDPC codeword are written in the five (5) columns inbits group wise and bits written in the same row in respective columnsare output serially. In this case, since 10 bits constitute a singlemodulation symbol in the modulation method of 1024-QAM, bits output fromthe two rows constitute a single modulation symbol. Accordingly, bitsincluded in a same bit group, that is, bits output from one column, maybe mapped onto two bits of a single modulation symbol. For example, bitsincluded in a bit group written in the first column may be mapped ontobits existing in two certain positions of a single modulation symbol.

Referring back to FIG. 1 , the modulator 130 maps the interleaved LDPCcodeword onto a modulation symbol. Specifically, the modulator 130 maydemultiplex the interleaved LDPC codeword, modulate the demultiplexedLDPC codeword, and map the LDPC codeword onto a constellation.

In this case, the modulator 130 may generate a modulation symbol usingbits included in each of a plurality of bit groups.

In other words, as described above, bits included in different bitgroups may be written in each column of the block interleaver 124, andthe block interleaver 124 reads the bits written in each column in therow direction. In this case, the modulator 130 generates a modulationsymbol by mapping bits read in each column onto each bit of themodulation symbol. Accordingly, each bit of the modulation symbol maybelong to a different group.

For example, it is assumed that a modulation symbol is formed of Cnumber of bits. In this case, bits which are read from each row of Cnumber of columns of the block interleaver 124 may be mapped onto eachbit of the modulation symbol and thus, each bit of the modulation symbolformed of C number of bits may belong to C number of different groups.

Hereinbelow, the above feature will be described in greater detail.

First, the modulator 130 may demultiplex the interleaved LDPC codeword.To achieve this, the modulator 130 may include a demultiplexer (notshown) to demultiplex the interleaved LDPC codeword.

A demultiplexer (not shown) demultiplexes the interleaved LDPC codeword.Specifically, the demultiplexer (not shown) performs serial-to-parallelconversion with respect to the interleaved LDPC codeword, anddemultiplexes the interleaved LDPC codeword into a cell having apredetermined number of bits (or a data cell).

For example, as shown in FIG. 13 , the demultiplexer (not shown)receives an LDPC codeword Q=(q₀, q₁, q₂, . . . ) output from theinterleaver 120, outputs the received LDPC codeword bits to a pluralityof substreams serially, converts the input LDPC codeword bits intocells, and outputs the cells.

Herein, the number of substreams, N_(substreams), may be equal to thenumber of bits constituting a modulation symbol, η_(MOD). Accordingly,the number of bits constituting each cell may be equal to the number ofbits constituting the modulation symbol (that is, a modulation order).

η_(MOD) may vary according to a modulation method and then number ofcells generated may vary according to the length N_(ldpc) of the LDPCcodeword as shown in Table 26.

TABLE 26 Number of output Number of output Modulation data cells fordata cells for mode μ_(MOD) N_(ldpc) = 64800 N_(ldpc) = 16200 QPSK 232400 8100 16-QAM 4 16200 4050 64-QAM 6 10800 2700 256-QAM  8 8100 20251024-QAM  10 6480 1620

In this case, bits having a same index in each of the plurality ofsubstreams may constitute a same cell. Accordingly, cells may beconfigured like (y_(0,0), y_(1,0), . . . , y_(η MOD−1,0))=(q₀, q₁,q_(η MOD−1)), (y_(0,1), y_(1,1), . . . , y_(η MOD−1,1))=(q_(η MOD),q_(η MOD+1), . . . , q_(2×η MOD−1)), . . . .

As described above, the number of substreams, N_(substreams), is equalto the number of bits constituting a modulation symbol, η_(MOD), and thenumber of bits constituting each cell may be equal to the number of bitsconstituting the modulation symbol.

The demultiplexer (not shown) may demultiplex input LDPC codeword bitsin various methods. That is, the demultiplexer (not shown) may change anorder of the LDPC codeword bits and output the bits to each of theplurality of substreams, or may output the bits to each of the pluralityof streams serially without changing the order of the LDPC codewordbits. These operations may be determined according to the number ofcolumns used for interleaving in the block interleaver 124.

Specifically, when the block interleaver 124 includes as many columns ashalf of the number of bits constituting the modulation symbol, thedemultiplexer (not shown) may change the order of the input LDPCcodeword bits and output the bits to each of the plurality ofsubstreams. An example of a method for changing the order is illustratedin Table 27 presented below:

TABLE 27 Modulation format QPSM input bit 0 1 di mod N_(substreams)output bit-number 0 1 Modulation format 16QAM input bit 0 1 2 3 di modN_(substreams) output bit-number 0 2 1 3 Modulation format 64 QAM inputbit 0 1 2 2 4 5 di mod N_(substreams) output bit-number 0 3 1 4 2 5Modulation format 256 QAM input bit 0 1 2 3 4 5 6 7 di modN_(substreams) output bit-number 0 4 1 5 2 6 3 7 Modulation format 1024QAM input bit 0 1 2 3 4 5 6 7 8 9 di mod N_(substreams) outputbit-number 0 5 1 6 2 7 3 5 4 9 Modulation format 4096 QAM input bit 0 12 3 4 5 6 7 8 9 10 11 di mod N_(substreams) output bit-number 0 6 1 7 26 3 9 4 10 5 11

According to Table 27, when the modulation method is 1024-QAM forexample, the number of substreams is 10 since the number of bitsconstituting a modulation symbol is 10 in the case of 1024-QAM. In thiscase, the demultiplexer (not shown) may output, from among the seriallyinput bits, bits with an index i satisfying i mod 10=0 to the 0^(th)substream, bits with an index i satisfying i mod 10=1 to the 5^(th)substream, bits with an index i satisfying i mode 10=2 to the 1^(st)substream, bits with an index i satisfying i mode 10=3 to the 6^(th)substream, bits with an index i satisfying i mode 10=4 to the 2^(nd)substream, bits with an index i satisfying i mode 10=5 to the 7^(th)substream, bits with an index i satisfying i mode 10=6 to the 3^(rd)substream, bits with an index i satisfying i mode 10=7 to the 8^(th)substream, bits with an index i satisfying i mode 10=8 to the 4^(th)substream, and bits with an index i satisfying i mode 10=9 to the 9^(th)substream.

Accordingly, the LDPC codeword bits input to the demultiplexer (notshown), (q₀, q₁, q₂, q₃, q₄, q₅, q₆, q₇, q₈, q₉, . . . ), may be outputas cells like (y_(0,0), y_(1,0), y_(2,0), y_(3,0), y_(4,0), y_(5,0),y_(6,0), y_(7,0), Y_(8,0), y_(9,0))=(q₀, q₅, q₁, q₆, q₂, q₇, q₃, q₈, q₄,q₉), (y_(0,1), y_(1,1), y_(2,1), Y_(3,1), Y_(4,1), y_(5,1), y_(6,1),y_(7,1), y_(8,1), y_(9,1))=(q₁₀, q₁₅, q₁₁, q₁₆, q₁₂, q₁₇, q₁₃, q₁₈, q₁₄,q₁₉), . . . .

When the block interleaver 124 includes the same number of columns asthe number of bits constituting a modulation symbol, the demultiplexer(not shown) may output the input LDPC codeword bits to each of theplurality of streams serially without changing the order of the bits.That is, as shown in FIG. 13 , the demultiplexer (not shown) may outputthe input LDPC codeword bits (q₀, q₁, q₂, . . . ) to each of thesubstreams serially, and accordingly, each cell may be configured as(y_(0,0), y_(1,0), . . . , y_(η MOD−1,0))=(q₀, q₁, . . . , q_(η MOD−1)),(y_(0,1), y_(1,1), . . . , y_(η MOD−1,1))=(q_(η MOD), q_(η MOD+1), . . ., q_(2×η MOD−1)), . . . .

For example, when the modulation method is 1024-QPSK, the number of bitsconstituting a modulation symbol, η_(MOD), is 10 and thus the number ofsubstreams, N_(substreams), is 10, and cells may be configured like(y_(0,0), y_(1,0), y_(2,0), y_(3,0), y_(4,0), y_(5,0), y_(6,0), y_(7,0),y_(8,0), y_(9,0))=(q₀, q₁, q₂, q₃, q₄, q₅, q₆, q₇, q₈, q₉), (y_(0,1),y_(1,1), y_(2,1), y_(3,1), y_(4,1), y_(5,1), y_(6,1), y_(7,1), y_(8,1),y_(9,1))=(q₁₀, q₁₁, q₁₂, q₁₃, q₁₄, q₁₅, q₁₆, q₁₇, q₁₈, q₁₉), (y_(0,2),y_(1,2), y_(2,2), y_(3,2), y_(4,2), y_(5,2), y_(6,2), y_(7,2), y_(8,2),y_(9,2))=(q₂₀, q₂₁, q₂₂, q₂₃, q₂₄, q₂₅, q₂₆, q₂₇, q₂₈, q₂₉)

In the above-described example, the demultiplexer (not shown) may outputthe input LDPC codeword bits to each of the plurality of substreamsserially without changing the order of the LDPC codeword bits. However,this is merely an example. According to an exemplary embodiment, whenthe block interleaver 124 includes the same number of columns as thenumber of bits of the modulation symbol, the demultiplexer (not shown)may be omitted.

The modulator 130 may map the demultiplexed LDPC codeword ontomodulation symbols. However, when the demultiplexer (not shown) isomitted as described, the modulator 130 may map the LDPC codeword bitsoutput from the interleaver 120, that is, the block-interleaved LDPCcodeword bits, onto the modulation symbols.

Specifically, the modulator 130 may modulate the bits (that is, cells)output from the demultiplexer (not shown) in various modulation methodssuch as QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM. Forexample, when the modulation method is QPSK, 16-QAM, 64-QAM, 256-QAM,1024-QAM, and 4096-QAM, the number of bits constituting the modulationsymbol, η_(MOD), may be 2, 4, 6, 8, 10 and 12, respectively.

In this case, since each cell output from the demultiplexer (not shown)is formed of as many bits as the number of bits constituting amodulation symbol, the modulator 130 may generate the modulation symbolby mapping each cell output from the demultiplexer (not shown) onto aconstellation point serially. Herein, a modulation symbol corresponds toa constellation point on the constellation.

However, the above-described demultiplexer (not shown) may be omittedaccording to circumstances. In this case, the modulator 130 may generatemodulation symbols by grouping a predetermined number of bits frominterleaved bits serially and mapping the predetermined number of bitsonto constellation points. In this case, the modulator 130 may generatethe modulation symbols by mapping η_(MOD) number of bits onto theconstellation points serially according to a modulation method.

The modulator 130 may modulate by mapping cells output from thedemultiplexer (not shown) onto constellation points in a non-uniformconstellation (NUC) method. For example, the modulator 130 may modulatebits output from the demultiplexer (not shown) in various modulationmethods such as non-uniform 16-QAM, non-uniform 64-QAM, non-uniform256-QAM, non-uniform 1024-QAM, non-uniform 4096-QAM, etc.

In the non-uniform constellation method, once a constellation point ofthe first quadrant is defined, constellation points in the other threequadrants may be determined as follows. For example, when a set ofconstellation points defined for the first quadrant is X, the set is−conj(X) in the case of the second quadrant, is conj(X) in the case ofthe third quadrant, and is −(X) in the case of the fourth quadrant.

That is, once the first quadrant is defined, the other quadrants may beexpressed as follows:

1 Quarter (first quadrant)=X

2 Quarter (second quadrant)=−conj(X)

3 Quarter (third quadrant)=conj(X)

4 Quarter (fourth quadrant)=−X

Specifically, when the non-uniform M-QAM is used, M number ofconstellation points may be defined as z={z₀, z₁, . . . , z_(M−1)}. Inthis case, when the constellation points existing in the first quadrantare defined as {x₀, x₁, x₂, . . . , x_(M/4-1)}, z may be defined asfollows:

from z₀ to z_(M/4−1)=from x₀ to x_(M/4)

from z_(M/4) to z_(2×M/4−1)=−conj(from x₀ to x_(M/4))

from z_(2×M/4) to z_(3×M/4−1)=conj(from x₀ to x_(M/4))

from z_(3×M/4) to z_(4×M/4−1)=−(from x₀ to x_(M/4))

Accordingly, the modulator 130 may map the bits [y₀, . . . , y_(m−1)]output from the demultiplexer (not shown) onto constellation points inthe non-uniform constellation method by mapping the output bits ontoz_(L) having an index of

${L = {\sum\limits_{i = 0}^{m - 1}\left( {y_{1} \times 2^{m - 1}} \right)}}.$

An example of the constellation defined according to the non-uniform1024-QAM method may be expressed as in Table 28 presented below when thecode rate is 6/15, 8/15, 10/15, 12/15. In this case, the constellationpoint of the first quadrant may be defined with reference to Table 28,and the constellation points in the other three quadrants may be definedin the above-described method.

TABLE 28 Label CR 6/15 CR 8/15 CR 10/15 CR 12/15 (int.) ConstellationConstellation Constellation Constellation 0 1.5031 + 1.5031i 1.4800 +1.4800i 1.4377 + 1.4377i 1.3675 + 1.3675i 1 1.5031 + 1.2286i 1.4800 +1.2281i 1.4377 + 1.2232i 1.3675 + 1.1917i 2 1.2286 + 1.5031i 1.2281 +1.4800i 1.2232 + 1.4377i 1.1917 + 1.3675i 3 1.2286 + 1.2286i 1.2281 +1.2281i 1.2232 + 1.2232i 1.1917 + 1.1917i 4 1.5031 + 0.9418i 1.4800 +0.9212i 1.4377 + 0.9302i 1.3675 + 0.9386i 5 1.5031 + 1.0048i 1.4800 +1.0349i 1.4377 + 1.0579i 1.3675 + 1.0529i 6 1.2286 + 0.9418i 1.2281 +0.9212i 1.2232 + 0.9302i 1.1917 + 0.9386i 7 1.2286 + 1.0048i 1.2281 +1.0349i 1.2232 + 1.0579i 1.1917 + 1.0529i 8 0.9418 + 1.5031i 0.9212 +1.4800i 0.9302 + 1.4377i 0.9386 + 1.3675i 9 0.9418 + 1.2286i 0.9212 +1.2281i 0.9302 + 1.2232i 0.9386 + 1.1917i 10 1.0048 + 1.5031i 1.0349 +1.4800i 1.0579 + 1.4377i 1.0529 + 1.3675i 11 1.0048 + 1.2286i 1.0349 +1.2281i 1.0579 + 1.2232i 1.0529 + 1.1917i 12 0.9418 + 0.9418i 0.9212 +0.9212i 0.9302 + 0.9302i 0.9386 + 0.9386i 13 0.9418 + 1.0048i 0.9212 +1.0349i 0.9302 + 1.0579i 0.9386 + 1.0529i 14 1.0048 + 0.9418i 1.0349 +0.9212i 1.0579 + 0.9302i 1.0529 + 0.9386i 15 1.0048 + 1.0048i 1.0349 +1.0349i 1.0579 + 1.0579i 1.0529 + 1.0529i 16 1.5031 + 0.6097i 1.4800 +0.5810i 1.4377 + 0.5505i 1.3675 + 0.5763i 17 1.5031 + 0.6072i 1.4800 +0.5872i 1.4377 + 0.6150i 1.3675 + 0.6531i 18 1.2286 + 0.6097i 1.2281 +0.5810i 1.2232 + 0.5505i 1.1917 + 0.5763i 19 1.2286 + 0.6072i 1.2281 +0.5872i 1.2232 + 0.6150i 1.1917 + 0.6531i 20 1.5031 + 0.7196i 1.4800 +0.7604i 1.4377 + 0.8066i 1.3675 + 0.8324i 21 1.5031 + 0.7113i 1.4800 +0.7213i 1.4377 + 0.7158i 1.3675 + 0.7417i 22 1.2286 + 0.7196i 1.2281 +0.7604i 1.2232 + 0.8066i 1.1917 + 0.8324i 23 1.2286 + 0.7113i 1.2281 +0.7213i 1.2232 + 0.7158i 1.1917 + 0.7417i 24 0.9418 + 0.6097i 0.9212 +0.5810i 0.9302 + 0.5505i 0.9386 + 0.5763i 25 0.9418 + 0.6072i 0.9212 +0.5872i 0.9302 + 0.6150i 0.9386 + 0.6531i 26 1.0048 + 0.6097i 1.0349 +0.5810i 1.0579 + 0.5505i 1.0529 + 0.5763i 27 1.0048 + 0.6072i 1.0349 +0.5872i 1.0579 + 0.6150i 1.0529 + 0.6531i 28 0.9418 + 0.7196i 0.9212 +0.7604i 0.9302 + 0.8066i 0.9386 + 0.8324i 29 0.9418 + 0.7113i 0.9212 +0.7213i 0.9302 + 0.7158i 0.9386 + 0.7417i 30 1.0048 + 0.7196i 1.0349 +0.7604i 1.0579 + 0.8066i 1.0529 + 0.8324i 31 1.0048 + 0.7113i 1.0349 +0.7213i 1.0579 + 0.7158i 1.0529 + 0.7417i 32 0.6097 + 1.5031i 0.5810 +1.4800i 0.5505 + 1.4377i 0.5763 + 1.3675i 33 0.6097 + 1.2286i 0.5810 +1.2281i 0.5505 + 1.2232i 0.5763 + 1.1917i 34 0.6072 + 1.5031i 0.5872 +1.4800i 0.6150 + 1.4377i 0.6531 + 1.3675i 35 0.6072 + 1.2286i 0.5872 +1.2281i 0.6150 + 1.2232i 0.6531 + 1.1917i 36 0.6097 + 0.9418i 0.5810 +0.9212i 0.5505 + 0.9302i 0.5763 + 0.9386i 37 0.6097 + 1.0048i 0.5810 +1.0349i 0.5505 + 1.0579i 0.5763 + 1.0529i 38 0.6072 + 0.9418i 0.5872 +0.9212i 0.6150 + 0.9302i 0.6531 + 0.9386i 39 0.6072 + 1.0048i 0.5872 +1.0349i 0.6150 + 1.0579i 0.6531 + 1.0529i 40 0.7196 + 1.5031i 0.7604 +1.4800i 0.8066 + 1.4377i 0.8324 + 1.3675i 41 0.7196 + 1.2286i 0.7604 +1.2281i 0.8066 + 1.2232i 0.8324 + 1.1917i 42 0.7113 + 1.5031i 0.7213 +1.4800i 0.7158 + 1.4377i 0.7417 + 1.3675i 43 0.7113 + 1.2286i 0.7213 +1.2281i 0.7158 + 1.2232i 0.7417 + 1.1917i 44 0.7196 + 0.9418i 0.7604 +0.9212i 0.8066 + 0.9302i 0.8324 + 0.9386i 45 0.7196 + 1.0048i 0.7604 +1.0349i 0.8066 + 1.0579i 0.8324 + 1.0529i 46 0.7113 + 0.9418i 0.7213 +0.9212i 0.7158 + 0.9302i 0.7417 + 0.9386i 47 0.7113 + 1.0048i 0.7213 +1.0349i 0.7158 + 1.0579i 0.7417 + 1.0529i 48 0.6097 + 0.6097i 0.5810 +0.5810i 0.5505 + 0.5505i 0.5763 + 0.5763i 49 0.6097 + 0.6072i 0.5810 +0.5872i 0.5505 + 0.6150i 0.5763 + 0.6531i 50 0.6072 + 0.6097i 0.5872 +0.5810i 0.6150 + 0.5505i 0.6531 + 0.5763i 51 0.6072 + 0.6072i 0.5872 +0.5872i 0.6150 + 0.6150i 0.6531 + 0.6531i 52 0.6097 + 0.7196i 0.5810 +0.7604i 0.5505 + 0.8066i 0.5763 + 0.8324i 53 0.6097 + 0.7113i 0.5810 +0.7213i 0.5505 + 0.7158i 0.5763 + 0.7417i 54 0.6072 + 0.7196i 0.5872 +0.7604i 0.6150 + 0.8066i 0.6531 + 0.8324i 55 0.6072 + 0.7113i 0.5872 +0.7213i 0.6150 + 0.7158i 0.6531 + 0.7417i 56 0.7196 + 0.6097i 0.7604 +0.5810i 0.8066 + 0.5505i 0.8324 + 0.5763i 57 0.7196 + 0.6072i 0.7604 +0.5872i 0.8066 + 0.6150i 0.8324 + 0.6531i 58 0.7113 + 0.6097i 0.7213 +0.5810i 0.7158 + 0.5505i 0.7417 + 0.5763i 59 0.7113 + 0.6072i 0.7213 +0.5872i 0.7158 + 0.6150i 0.7417 + 0.6531i 60 0.7196 + 0.7196i 0.7604 +0.7604i 0.8066 + 0.8066i 0.8324 + 0.8324i 61 0.7196 + 0.7113i 0.7604 +0.7213i 0.8066 + 0.7158i 0.8324 + 0.7417i 62 0.7113 + 0.7196i 0.7213 +0.7604i 0.7158 + 0.8066i 0.7417 + 0.8324i 63 0.7113 + 0.7113i 0.7213 +0.7213i 0.7158 + 0.7158i 0.7417 + 0.7417i 64 1.5031 + 0.1275i 1.4800 +0.0773i 1.4377 + 0.0596i 1.3675 + 0.0354i 65 1.5031 + 0.1276i 1.4800 +0.0773i 1.4377 + 0.0642i 1.3675 + 0.0921i 66 1.2286 + 0.1275i 1.2281 +0.0773i 1.2232 + 0.0596i 1.1917 + 0.0354i 67 1.2286 + 0.1276i 1.2281 +0.0773i 1.2232 + 0.0642i 1.1917 + 0.0921i 68 1.5031 + 0.1295i 1.4800 +0.1614i 1.4377 + 0.1766i 1.3675 + 0.2185i 69 1.5031 + 0.1294i 1.4800 +0.1614i 1.4377 + 0.1669i 1.3675 + 0.1602i 70 1.2286 + 0.1295i 1.2281 +0.1614i 1.2232 + 0.1766i 1.1917 + 0.2185i 71 1.2286 + 0.1294i 1.2281 +0.1614i 1.2232 + 0.1669i 1.1917 + 0.1602i 72 0.9418 + 0.1275i 0.9212 +0.0773i 0.9302 + 0.0596i 0.9386 + 0.0354i 73 0.9418 + 0.1276i 0.9212 +0.0773i 0.9302 + 0.0642i 0.9386 + 0.0921i 74 1.0048 + 0.1275i 1.0349 +0.0773i 1.0579 + 0.0596i 1.0529 + 0.0354i 75 1.0048 + 0.1276i 1.0349 +0.0773i 1.0579 + 0.0642i 1.0529 + 0.0921i 76 0.9418 + 0.1295i 0.9212 +0.1614i 0.9302 + 0.1766i 0.9386 + 0.2185i 77 0.9418 + 0.1294i 0.9212 +0.1614i 0.9302 + 0.1669i 0.9386 + 0.1602i 78 1.0048 + 0.1295i 1.0349 +0.1614i 1.0579 + 0.1766i 1.0529 + 0.2185i 79 1.0048 + 0.1294i 1.0349 +0.1614i 1.0579 + 0.1669i 1.0529 + 0.1602i 80 1.5031 + 0.3666i 1.4800 +0.4163i 1.4377 + 0.4471i 1.3675 + 0.4947i 81 1.5031 + 0.3675i 1.4800 +0.4159i 1.4377 + 0.4043i 1.3675 + 0.4264i 82 1.2286 + 0.3666i 1.2281 +0.4163i 1.2232 + 0.4471i 1.1917 + 0.4947i 83 1.2286 + 0.3675i 1.2281 +0.4159i 1.2232 + 0.4043i 1.1917 + 0.4264i 84 1.5031 + 0.3424i 1.4800 +0.3086i 1.4377 + 0.2868i 1.3675 + 0.2910i 85 1.5031 + 0.3431i 1.4800 +0.3085i 1.4377 + 0.3091i 1.3675 + 0.3530i 86 1.2286 + 0.3424i 1.2281 +0.3086i 1.2232 + 0.2868i 1.1917 + 0.2910i 87 1.2286 + 0.3431i 1.2281 +0.3085i 1.2232 + 0.3091i 1.1917 + 0.3530i 88 0.9418 + 0.3666i 0.9212 +0.4163i 0.9302 + 0.4471i 0.9386 + 0.4947i 89 0.9418 + 0.3675i 0.9212 +0.4159i 0.9302 + 0.4043i 0.9386 + 0.4264i 90 1.0048 + 0.3666i 1.0349 +0.4163i 1.0579 + 0.4471i 1.0529 + 0.4947i 91 1.0048 + 0.3675i 1.0349 +0.4159i 1.0579 + 0.4043i 1.0529 + 0.4264i 92 0.9418 + 0.3424i 0.9212 +0.3086i 0.9302 + 0.2868i 0.9386 + 0.2910i 93 0.9418 + 0.3431i 0.9212 +0.3085i 0.9302 + 0.3091i 0.9386 + 0.3530i 94 1.0048 + 0.3424i 1.0349 +0.3086i 1.0579 + 0.2868i 1.0529 + 0.2910i 95 1.0048 + 0.3431i 1.0349 +0.3085i 1.0579 + 0.3091i 1.0529 + 0.3530i 96 0.6097 + 0.1275i 0.5810 +0.0773i 0.5505 + 0.0596i 0.5763 + 0.0354i 97 0.6097 + 0.1276i 0.5810 +0.0773i 0.5505 + 0.0642i 0.5763 + 0.0921i 98 0.6072 + 0.1275i 0.5872 +0.0773i 0.6150 + 0.0596i 0.6531 + 0.0354i 99 0.6072 + 0.1276i 0.5872 +0.0773i 0.6150 + 0.0642i 0.6531 + 0.0921i 100 0.6097 + 0.1295i 0.5810 +0.1614i 0.5505 + 0.1766i 0.5763 + 0.2185i 101 0.6097 + 0.1294i 0.5810 +0.1614i 0.5505 + 0.1669i 0.5763 + 0.1602i 102 0.6072 + 0.1295i 0.5872 +0.1614i 0.6150 + 0.1766i 0.6531 + 0.2185i 103 0.6072 + 0.1294i 0.5872 +0.1614i 0.6150 + 0.1669i 0.6531 + 0.1602i 104 0.7196 + 0.1275i 0.7604 +0.0773i 0.8066 + 0.0596i 0.8324 + 0.0354i 105 0.7196 + 0.1276i 0.7604 +0.0773i 0.8066 + 0.0642i 0.8324 + 0.0921i 106 0.7113 + 0.1275i 0.7213 +0.0773i 0.7158 + 0.0596i 0.7417 + 0.0354i 107 0.7113 + 0.1276i 0.7213 +0.0773i 0.7158 + 0.0642i 0.7417 + 0.0921i 108 0.7196 + 0.1295i 0.7604 +0.1614i 0.8066 + 0.1766i 0.8324 + 0.2185i 109 0.7196 + 0.1294i 0.7604 +0.1614i 0.8066 + 0.1669i 0.8324 + 0.1602i 110 0.7113 + 0.1295i 0.7213 +0.1614i 0.7158 + 0.1766i 0.7417 + 0.2185i 111 0.7113 + 0.1294i 0.7213 +0.1614i 0.7158 + 0.1669i 0.7417 + 0.1602i 112 0.6097 + 0.3666i 0.5810 +0.4163i 0.5505 + 0.4471i 0.5763 + 0.4947i 113 0.6097 + 0.3675i 0.5810 +0.4159i 0.5505 + 0.4043i 0.5763 + 0.4264i 114 0.6072 + 0.3666i 0.5872 +0.4163i 0.6150 + 0.4471i 0.6531 + 0.4947i 115 0.6072 + 0.3675i 0.5872 +0.4159i 0.6150 + 0.4043i 0.6531 + 0.4264i 116 0.6097 + 0.3424i 0.5810 +0.3086i 0.5505 + 0.2868i 0.5763 + 0.2910i 117 0.6097 + 0.3431i 0.5810 +0.3085i 0.5505 + 0.3091i 0.5763 + 0.3530i 118 0.6072 + 0.3424i 0.5872 +0.3086i 0.6150 + 0.2868i 0.6531 + 0.2910i 119 0.6072 + 0.3431i 0.5872 +0.3085i 0.6150 + 0.3091i 0.6531 + 0.3530i 120 0.7196 + 0.3666i 0.7604 +0.4163i 0.8066 + 0.4471i 0.8324 + 0.4947i 121 0.7196 + 0.3675i 0.7604 +0.4159i 0.8066 + 0.4043i 0.8324 + 0.4264i 122 0.7113 + 0.3666i 0.7213 +0.4163i 0.7158 + 0.4471i 0.7417 + 0.4947i 123 0.7113 + 0.3675i 0.7213 +0.4159i 0.7158 + 0.4043i 0.7417 + 0.4264i 124 0.7196 + 0.3424i 0.7604 +0.3086i 0.8066 + 0.2868i 0.8324 + 0.2910i 125 0.7196 + 0.3431i 0.7604 +0.3085i 0.8066 + 0.3091i 0.8324 + 0.3530i 126 0.7113 + 0.3424i 0.7213 +0.3086i 0.7158 + 0.2868i 0.7417 + 0.2910i 127 0.7113 + 0.3431i 0.7213 +0.3085i 0.7158 + 0.3091i 0.7417 + 0.3530i 128 0.1275 + 1.5031i 0.0773 +1.4800i 0.0596 + 1.4377i 0.0354 + 1.3675i 129 0.1275 + 1.2286i 0.0773 +1.2281i 0.0596 + 1.2232i 0.0354 + 1.1917i 130 0.1276 + 1.5031i 0.0773 +1.4800i 0.0642 + 1.4377i 0.0921 + 1.3675i 131 0.1276 + 1.2286i 0.0773 +1.2281i 0.0642 + 1.2232i 0.0921 + 1.1917i 132 0.1275 + 0.9418i 0.0773 +0.9212i 0.0596 + 0.9302i 0.0354 + 0.9386i 133 0.1275 + 1.0048i 0.0773 +1.0349i 0.0596 + 1.0579i 0.0354 + 1.0529i 134 0.1276 + 0.9418i 0.0773 +0.9212i 0.0642 + 0.9302i 0.0921 + 0.9386i 135 0.1276 + 1.0048i 0.0773 +1.0349i 0.0642 + 1.0579i 0.0921 + 1.0529i 136 0.1295 + 1.5031i 0.1614 +1.4800i 0.1766 + 1.4377i 0.2185 + 1.3675i 137 0.1295 + 1.2286i 0.1614 +1.2281i 0.1766 + 1.2232i 0.2185 + 1.1917i 138 0.1294 + 1.5031i 0.1614 +1.4800i 0.1669 + 1.4377i 0.1602 + 1.3675i 139 0.1294 + 1.2286i 0.1614 +1.2281i 0.1669 + 1.2232i 0.1602 + 1.1917i 140 0.1295 + 0.9418i 0.1614 +0.9212i 0.1766 + 0.9302i 0.2185 + 0.9386i 141 0.1295 + 1.0048i 0.1614 +1.0349i 0.1766 + 1.0579i 0.2185 + 1.0529i 142 0.1294 + 0.9418i 0.1614 +0.9212i 0.1669 + 0.9302i 0.1602 + 0.9386i 143 0.1294 + 1.0048i 0.1614 +1.0349i 0.1669 + 1.0579i 0.1602 + 1.0529i 144 0.1275 + 0.6097i 0.0773 +0.5810i 0.0596 + 0.5505i 0.0354 + 0.5763i 145 0.1275 + 0.6072i 0.0773 +0.5872i 0.0596 + 0.6150i 0.0354 + 0.6531i 146 0.1276 + 0.6097i 0.0773 +0.5810i 0.0642 + 0.5505i 0.0921 + 0.5763i 147 0.1276 + 0.6072i 0.0773 +0.5872i 0.0642 + 0.6150i 0.0921 + 0.6531i 148 0.1275 + 0.7196i 0.0773 +0.7604i 0.0596 + 0.8066i 0.0354 + 0.8324i 149 0.1275 + 0.7113i 0.0773 +0.7213i 0.0596 + 0.7158i 0.0354 + 0.7417i 150 0.1276 + 0.7196i 0.0773 +0.7604i 0.0642 + 0.8066i 0.0921 + 0.8324i 151 0.1276 + 0.7113i 0.0773 +0.7213i 0.0642 + 0.7158i 0.0921 + 0.7417i 152 0.1295 + 0.6097i 0.1614 +0.5810i 0.1766 + 0.5505i 0.2185 + 0.5763i 153 0.1295 + 0.6072i 0.1614 +0.5872i 0.1766 + 0.6150i 0.2185 + 0.6531i 154 0.1294 + 0.6097i 0.1614 +0.5810i 0.1669 + 0.5505i 0.1602 + 0.5763i 155 0.1294 + 0.6072i 0.1614 +0.5872i 0.1669 + 0.6150i 0.1602 + 0.6531i 156 0.1295 + 0.7196i 0.1614 +0.7604i 0.1766 + 0.8066i 0.2185 + 0.8324i 157 0.1295 + 0.7113i 0.1614 +0.7213i 0.1766 + 0.7158i 0.2185 + 0.7417i 158 0.1294 + 0.7196i 0.1614 +0.7604i 0.1669 + 0.8066i 0.1602 + 0.8324i 159 0.1294 + 0.7113i 0.1614 +0.7213i 0.1669 + 0.7158i 0.1602 + 0.7417i 160 0.3666 + 1.5031i 0.4163 +1.4800i 0.4471 + 1.4377i 0.4947 + 1.3675i 161 0.3666 + 1.2286i 0.4163 +1.2281i 0.4471 + 1.2232i 0.4947 + 1.1917i 162 0.3675 + 1.5031i 0.4159 +1.4800i 0.4043 + 1.4377i 0.4264 + 1.3675i 163 0.3675 + 1.2286i 0.4159 +1.2281i 0.4043 + 1.2232i 0.4264 + 1.1917i 164 0.3666 + 0.9418i 0.4163 +0.9212i 0.4471 + 0.9302i 0.4947 + 0.9386i 165 0.3666 + 1.0048i 0.4163 +1.0349i 0.4471 + 1.0579i 0.4947 + 1.0529i 166 0.3675 + 0.9418i 0.4159 +0.9212i 0.4043 + 0.9302i 0.4264 + 0.9386i 167 0.3675 + 1.0048i 0.4159 +1.0349i 0.4043 + 1.0579i 0.4264 + 1.0529i 168 0.3424 + 1.5031i 0.3086 +1.4800i 0.2868 + 1.4377i 0.2910 + 1.3675i 169 0.3424 + 1.2286i 0.3086 +1.2281i 0.2868 + 1.2232i 0.2910 + 1.1917i 170 0.3431 + 1.5031i 0.3085 +1.4800i 0.3091 + 1.4377i 0.3530 + 1.3675i 171 0.3431 + 1.2286i 0.3085 +1.2281i 0.3091 + 1.2232i 0.3530 + 1.1917i 172 0.3424 + 0.9418i 0.3086 +0.9212i 0.2868 + 0.9302i 0.2910 + 0.9386i 173 0.3424 + 1.0048i 0.3086 +1.0349i 0.2868 + 1.0579i 0.2910 + 1.0529i 174 0.3431 + 0.9418i 0.3085 +0.9212i 0.3091 + 0.9302i 0.3530 + 0.9386i 175 0.3431 + 1.0048i 0.3085 +1.0349i 0.3091 + 1.0579i 0.3530 + 1.0529i 176 0.3666 + 0.6097i 0.4163 +0.5810i 0.4471 + 0.5505i 0.4947 + 0.5763i 177 0.3666 + 0.6072i 0.4163 +0.5872i 0.4471 + 0.6150i 0.4947 + 0.6531i 178 0.3675 + 0.6097i 0.4159 +0.5810i 0.4043 + 0.5505i 0.4264 + 0.5763i 179 0.3675 + 0.6072i 0.4159 +0.5872i 0.4043 + 0.6150i 0.4264 + 0.6531i 180 0.3666 + 0.7196i 0.4163 +0.7604i 0.4471 + 0.8066i 0.4947 + 0.8324i 181 0.3666 + 0.7113i 0.4163 +0.7213i 0.4471 + 0.7158i 0.4947 + 0.7417i 182 0.3675 + 0.7196i 0.4159 +0.7604i 0.4043 + 0.8066i 0.4264 + 0.8324i 183 0.3675 + 0.7113i 0.4159 +0.7213i 0.4043 + 0.7158i 0.4264 + 0.7417i 184 0.3424 + 0.6097i 0.3086 +0.5810i 0.2868 + 0.5505i 0.2910 + 0.5763i 185 0.3424 + 0.6072i 0.3086 +0.5872i 0.2868 + 0.6150i 0.2910 + 0.6531i 186 0.3431 + 0.6097i 0.3085 +0.5810i 0.3091 + 0.5505i 0.3530 + 0.5763i 187 0.3431 + 0.6072i 0.3085 +0.5872i 0.3091 + 0.6150i 0.3530 + 0.6531i 188 0.3424 + 0.7196i 0.3086 +0.7604i 0.2868 + 0.8066i 0.2910 + 0.8324i 189 0.3424 + 0.7113i 0.3086 +0.7213i 0.2868 + 0.7158i 0.2910 + 0.7417i 190 0.3431 + 0.7196i 0.3085 +0.7604i 0.3091 + 0.8066i 0.3530 + 0.8324i 191 0.3431 + 0.7113i 0.3085 +0.7213i 0.3091 + 0.7158i 0.3530 + 0.7417i 192 0.1275 + 0.1275i 0.0773 +0.0773i 0.0596 + 0.0596i 0.0354 + 0.0354i 193 0.1275 + 0.1276i 0.0773 +0.0773i 0.0596 + 0.0642i 0.0354 + 0.0921i 194 0.1276 + 0.1275i 0.0773 +0.0773i 0.0642 + 0.0596i 0.0921 + 0.0354i 195 0.1276 + 0.1276i 0.0773 +0.0773i 0.0642 + 0.0642i 0.0921 + 0.0921i 196 0.1275 + 0.1295i 0.0773 +0.1614i 0.0596 + 0.1766i 0.0354 + 0.2185i 197 0.1275 + 0.1294i 0.0773 +0.1614i 0.0596 + 0.1669i 0.0354 + 0.1602i 198 0.1276 + 0.1295i 0.0773 +0.1614i 0.0642 + 0.1766i 0.0921 + 0.2185i 199 0.1276 + 0.1294i 0.0773 +0.1614i 0.0642 + 0.1669i 0.0921 + 0.1602i 200 0.1295 + 0.1275i 0.1614 +0.0773i 0.1766 + 0.0596i 0.2185 + 0.0354i 201 0.1295 + 0.1276i 0.1614 +0.0773i 0.1766 + 0.0642i 0.2185 + 0.0921i 202 0.1294 + 0.1275i 0.1614 +0.0773i 0.1669 + 0.0596i 0.1602 + 0.0354i 203 0.1294 + 0.1276i 0.1614 +0.0773i 0.1669 + 0.0642i 0.1602 + 0.0921i 204 0.1295 + 0.1295i 0.1614 +0.1614i 0.1766 + 0.1766i 0.2185 + 0.2185i 205 0.1295 + 0.1294i 0.1614 +0.1614i 0.1766 + 0.1669i 0.2185 + 0.1602i 206 0.1294 + 0.1295i 0.1614 +0.1614i 0.1669 + 0.1766i 0.1602 + 0.2185i 207 0.1294 + 0.1294i 0.1614 +0.1614i 0.1669 + 0.1669i 0.1602 + 0.1602i 208 0.1275 + 0.3666i 0.0773 +0.4163i 0.0596 + 0.4471i 0.0354 + 0.4947i 209 0.1275 + 0.3675i 0.0773 +0.4159i 0.0596 + 0.4043i 0.0354 + 0.4264i 210 0.1276 + 0.3666i 0.0773 +0.4163i 0.0642 + 0.4471i 0.0921 + 0.4947i 211 0.1276 + 0.3675i 0.0773 +0.4159i 0.0642 + 0.4043i 0.0921 + 0.4264i 212 0.1275 + 0.3424i 0.0773 +0.3086i 0.0596 + 0.2868i 0.0354 + 0.2910i 213 0.1275 + 0.3431i 0.0773 +0.3085i 0.0596 + 0.3091i 0.0354 + 0.3530i 214 0.1276 + 0.3424i 0.0773 +0.3086i 0.0642 + 0.2868i 0.0921 + 0.2910i 215 0.1276 + 0.3431i 0.0773 +0.3085i 0.0642 + 0.3091i 0.0921 + 0.3530i 216 0.1295 + 0.3666i 0.1614 +0.4163i 0.1766 + 0.4471i 0.2185 + 0.4947i 217 0.1295 + 0.3675i 0.1614 +0.4159i 0.1766 + 0.4043i 0.2185 + 0.4264i 218 0.1294 + 0.3666i 0.1614 +0.4163i 0.1669 + 0.4471i 0.1602 + 0.4947i 219 0.1294 + 0.3675i 0.1614 +0.4159i 0.1669 + 0.4043i 0.1602 + 0.4264i 220 0.1295 + 0.3424i 0.1614 +0.3086i 0.1766 + 0.2868i 0.2185 + 0.2910i 221 0.1295 + 0.3431i 0.1614 +0.3085i 0.1766 + 0.3091i 0.2185 + 0.3530i 222 0.1294 + 0.3424i 0.1614 +0.3086i 0.1669 + 0.2868i 0.1602 + 0.2910i 223 0.1294 + 0.3431i 0.1614 +0.3085i 0.1669 + 0.3091i 0.1602 + 0.3530i 224 0.3666 + 0.1275i 0.4163 +0.0773i 0.4471 + 0.0596i 0.4947 + 0.0354i 225 0.3666 + 0.1276i 0.4163 +0.0773i 0.4471 + 0.0642i 0.4947 + 0.0921i 226 0.3675 + 0.1275i 0.4159 +0.0773i 0.4043 + 0.0596i 0.4264 + 0.0354i 227 0.3675 + 0.1276i 0.4159 +0.0773i 0.4043 + 0.0642i 0.4264 + 0.0921i 228 0.3666 + 0.1295i 0.4163 +0.1614i 0.4471 + 0.1766i 0.4947 + 0.2185i 229 0.3666 + 0.1294i 0.4163 +0.1614i 0.4471 + 0.1669i 0.4947 + 0.1602i 230 0.3675 + 0.1295i 0.4159 +0.1614i 0.4043 + 0.1766i 0.4264 + 0.2185i 231 0.3675 + 0.1294i 0.4159 +0.1614i 0.4043 + 0.1669i 0.4264 + 0.1602i 232 0.3424 + 0.1275i 0.3086 +0.0773i 0.2868 + 0.0596i 0.2910 + 0.0354i 233 0.3424 + 0.1276i 0.3086 +0.0773i 0.2868 + 0.0642i 0.2910 + 0.0921i 234 0.3431 + 0.1275i 0.3085 +0.0773i 0.3091 + 0.0596i 0.3530 + 0.0354i 235 0.3431 + 0.1276i 0.3085 +0.0773i 0.3091 + 0.0642i 0.3530 + 0.0921i 236 0.3424 + 0.1295i 0.3086 +0.1614i 0.2868 + 0.1766i 0.2910 + 0.2185i 237 0.3424 + 0.1294i 0.3086 +0.1614i 0.2868 + 0.1669i 0.2910 + 0.1602i 238 0.3431 + 0.1295i 0.3085 +0.1614i 0.3091 + 0.1766i 0.3530 + 0.2185i 239 0.3431 + 0.1294i 0.3085 +0.1614i 0.3091 + 0.1669i 0.3530 + 0.1602i 240 0.3666 + 0.3666i 0.4163 +0.4163i 0.4471 + 0.4471i 0.4947 + 0.4947i 241 0.3666 + 0.3675i 0.4163 +0.4159i 0.4471 + 0.4043i 0.4947 + 0.4264i 242 0.3675 + 0.3666i 0.4159 +0.4163i 0.4043 + 0.4471i 0.4264 + 0.4947i 243 0.3675 + 0.3675i 0.4159 +0.4159i 0.4043 + 0.4043i 0.4264 + 0.4264i 244 0.3666 + 0.3424i 0.4163 +0.3086i 0.4471 + 0.2868i 0.4947 + 0.2910i 245 0.3666 + 0.3431i 0.4163 +0.3085i 0.4471 + 0.3091i 0.4947 + 0.3530i 246 0.3675 + 0.3424i 0.4159 +0.3086i 0.4043 + 0.2868i 0.4264 + 0.2910i 247 0.3675 + 0.3431i 0.4159 +0.3085i 0.4043 + 0.3091i 0.4264 + 0.3530i 248 0.3424 + 0.3666i 0.3086 +0.4163i 0.2868 + 0.4471i 0.2910 + 0.4947i 249 0.3424 + 0.3675i 0.3086 +0.4159i 0.2868 + 0.4043i 0.2910 + 0.4264i 250 0.3431 + 0.3666i 0.3085 +0.4163i 0.3091 + 0.4471i 0.3530 + 0.4947i 251 0.3431 + 0.3675i 0.3085 +0.4159i 0.3091 + 0.4043i 0.3530 + 0.4264i 252 0.3424 + 0.3424i 0.3086 +0.3086i 0.2868 + 0.2868i 0.2910 + 0.2910i 253 0.3424 + 0.3431i 0.3086 +0.3085i 0.2868 + 0.3091i 0.2910 + 0.3530i 254 0.3431 + 0.3424i 0.3085 +0.3086i 0.3091 + 0.2868i 0.3530 + 0.2910i 255 0.3431 + 0.3431i 0.3085 +0.3085i 0.3091 + 0.3091i 0.3530 + 0.3530i

Table 28 shows an example of constellation defined according to thenon-uniform 1024-QAM. However, this is merely an example. Theconstellation points may be defined variously in the non-uniform1024-QAM. In addition, the constellation points may be defined variouslyin the other modulation methods such as non-uniform 16-QAM, non-uniform64-QAM, non-uniform 256-QAM, non-uniform 4096-QAM, etc.

The interleaving is performed in the above-described method for thefollowing reasons.

Specifically, when LDPC codeword bits are mapped onto a modulationsymbol, the bits may have different reliability (that is, differentreceiving performance or different probability of reception) accordingto where the bits are mapped in the modulation symbol. The LDPC codewordbits may have different codeword characteristics according to theconfiguration of a parity check matrix. That is, the LDPC codeword bitsmay have different codeword characteristics according to the number of 1existing in the column of the parity check matrix, that is, the columndegree.

Accordingly, the interleaver 120 may interleave to map the LDPC codewordbits having a specific codeword characteristic onto specific bits in themodulation symbol by considering both the codeword characteristics ofthe LDPC codeword bits and the reliability of the bits constituting themodulation symbol.

For example, it is assumed that the encoder 110 generates an LDPCcodeword formed of 64800 bits (N_(ldpc)=64800) by LDPC encoding using acode rate of 6/15, and the modulator 130 uses the non-uniform 1024-QAMmodulation method corresponding to the code rate of 6/15 based on Table28.

In this case, the group interleaver 122 may perform group-interleavingusing Equation 15 and Table 9 (or Equation 16 and Table 15).Accordingly, the LDPC codeword formed of bit groups X₀ to X₁₇₉ isinterleaved by the group interleaver 122 and the group interleaver 122may output the bit groups in the order of X₆₆, X₂₁, X₅₁, . . . , X₁₁₆,X₁₂₃.

In this case, the number of columns constituting the block interleaver124 may be 10 and each column may be formed of 6480 (=360×18) rows. Thatis, the number of rows of the first part may be 6480 and the number ofrows of the second part may be 0.

Accordingly, from among the 180 groups constituting the LDPC codeword,18 bit groups (X₆₆, X₂₁, X₅₁, X₅₅, X₅₄, X₂₄, X₃₃, X₁₂, X₇₀, X₆₃, X₄₇,X₆₅, X₁₄₅, X₈, X₀, X₅₇, X₂₃, X₇₁) may be inputted to the first part ofthe 1^(st) column of the block interleaver 124, 18 bit groups (X₅₉, X₁₄,X₄₀, X₄₂, X₆₂, X₅₆, X₂, X₄₃, X₆₄, X₅₈, X₆₇, X₅₃, X₆₈, X₆₁, X₃₉, X₅₂,X₆₉, X₁) may be inputted to the first part of the 2^(nd) column of theblock interleaver 124, 18 bit groups (X₂₂, X₃₁, X₁₆₁, X₃₈, X₃₀, X₁₉,X₁₇, X₁₈, X₄, X₄₁, X₂₅, X₄₄, X₁₃₆, X₂₉, X₃₆, X₂₆, X₁₂₆, X₁₇₇) may beinputted to the first part of the 3^(rd) column of the block interleaver124, 18 bit groups (X₁₅, X₃₇, X₁₄₈, X₉, X₁₃, X₄₅, X₄₆, X₁₅₂, X₅₀, X₄₉,X₂₇, X₇₇, X₆₀, X₃₅, X₄₈, X₁₇₈, X₂₈, X₃₄) may be inputted to the firstpart of the 4^(th) column of the block interleaver 124, 18 bit groups(X₁₀₆, X₁₂₇, X₇₆, X₁₃₁, X₁₀₅, X₁₃₈, X₇₅, X₁₃₀, X₁₀₁, X₁₆₇, X₁₁₇, X₁₇₃,X₁₁₃, X₁₀₈, X₉₂, X₁₃₅, X₁₂₄, X₁₂₁) may be inputted to the first part ofthe 5^(th) column of the block interleaver 124, 18 bit groups (X₉₇,X₁₄₉, X₁₄₃, X₈₁, X₃₂, X₉₆, X₃, X₇₈, X₁₀₇, X₈₆, X₉₈, X₁₆, X₁₆₂, X₁₅₀,X₁₁₁, X₁₅₈, X₁₇₂, X₁₃₉) may be inputted to the first part of the 6^(th)column of the block interleaver 124, 18 bit groups (X₇₄, X₁₄₂, X₁₆₆, X₇,X₅, X₁₁₉, X₂₀, X₁₄₄, X₁₅₁, X₉₀, X₁₁, X₁₅₆, X₁₀₀, X₁₇₅, X₈₃, X₁₅₅, X₁₅₉,X₁₂₈) may be inputted to the first part of the 7^(th) column of theblock interleaver 124, 18 bit groups (X₈₈, X₈₇, X₉₃, X₁₀₃, X₉₄, X₁₄₀,X₁₆₅, X₆, X₁₃₇, X₁₅₇, X₁₀, X₈₅, X₁₄₁, X₁₂₉, X₁₄₆, X₁₂₂, X₇₃, X₁₁₂) maybe inputted to the first part of the 8^(th) column of the blockinterleaver 124, 18 bit groups (X₁₃₂, X₁₂₅, X₁₇₄, X₁₆₉, X₁₆₈, X₇₉, X₈₄,X₁₁₈, X₁₇₉, X₁₄₇, X₉₁, X₁₆₀, X₁₆₃, X₁₁₅, X₈₉, X₈₀, X₁₀₂, X₁₀₄) may beinputted to the first part of the 9^(th) column of the block interleaver124, and 18 bit groups (X₁₃₄, X₈₂, X₉₅, X₁₃₃, X₁₆₄, X₁₅₄, X₁₂₀, X₁₁₀,X₁₇₀, X₁₁₄, X₁₅₃, X₇₂, X₁₀₉, X₁₇₁, X₁₇₆, X₉₉, X₁₁₆, X₁₂₃) may beinputted to the first part of the 10^(th) column of the blockinterleaver 124.

In addition, the block interleaver 124 may output the bits inputted tothe 1^(st) row to the last row of each column serially, and the bitsoutputted from the block interleaver 124 may be inputted to themodulator 130 serially. In this case, the demultiplexer (not shown) maybe omitted or the demultiplexer (not shown) may output the inputted bitsserially without changing the order of bits.

Accordingly, one bit included in each of the bit groups X₆₆, X₅₉, X₂₂,X₁₅, X₁₀₆, X₉₇, X₇₄, X₈₈, X₁₃₂, and X₁₃₄ may constitute one modulationsymbol.

As described above, since a specific bit is mapped onto a specific bitin a modulation symbol through interleaving, a receiver side can achievehigh receiving performance and high decoding performance.

That is, when LDPC codeword bits of high decoding performance are mappedonto high reliability bits from among bits of each modulation symbol,the receiver side may show high decoding performance, but there is aproblem that the LDPC codeword bits of the high decoding performance arenot received. In addition, when the LDPC codeword bits of high decodingperformance are mapped onto low reliability bits from among the bits ofthe modulation symbol, initial receiving performance is excellent, andthus, overall performance is also excellent. However, when many bitsshowing poor decoding performance are received, error propagation mayoccur.

Accordingly, when LDPC codeword bits are mapped onto modulation symbols,an LDPC codeword bit having a specific codeword characteristic is mappedonto a specific bit of a modulation symbol by considering both codewordcharacteristics of the LDPC codeword bits and reliability of the bits ofthe modulation symbol, and is transmitted to the receiver side.Accordingly, the receiver side can achieve both the high receivingperformance and the high decoding performance.

The above-described group interleaving and block interleaving is merelyan example. In addition to the above-described method, other methods formaking one bit included in each of the bit groups X₆₆, X₅₉, X₂₂, X₁₅,X₁₀₆, X₉₇, X₇₄, X₈₈, X₁₃₂, and X₁₃₄ constitute one modulation symbol arecovered by the inventive concept.

Hereinafter, a method for determining π(j), which is a parameter usedfor group interleaving, according to various exemplary embodiments, willbe explained. First, criteria to be considered are as follows:

Criterion 1) A different interleaving order is used according to amodulation method and a code rate.

Criterion 2) A performance characteristic for each bit group of the LDPCcodeword and a performance characteristic for each bit of a modulationsymbol should be considered simultaneously.

For example, in the case of the LDPC codeword, the leftmost bits may begood in performance, and the leftmost bits of the modulation symbol maybe good in performance. That is, the relative size of receivingperformance P(y_(i)) of each of the 10 bits constituting the non-uniform1024-QAM, y₀, y₁, y₂, y₃, y₄, y₅, y₆, y₇, y₈, and y₉, has a relationshipof P(y₀)=P(y₁)≥P(y₂)=P(y₃)≥P(y₄)=P(y₅)≥P(y₆)=P(y₇)≥P(y₈)=P(y₉).

Therefore, when the length of the LDPC codeword is 64800 and thenon-uniform 1024-QAM (or 1024-NUC) is used, onto which bits from amongthe 10 bits of the non-uniform 1024-QAM the 180 LDPC bit groups aremapped is determined by considering the characteristics of the LDPCcodeword and the modulation method simultaneously. In this case, a casehaving the best estimated performance is determined using a Densityevolution method.

That is, a plurality of cases in which 180 bit groups are mapped ontothe 10 bits may be considered and a theoretically estimated thresholdvalue may be calculated by applying the density evolution method to eachcase. When an LDPC code is transmitted as an SNR value, an errorprobability is 0 in an SNR area greater than the threshold value.Therefore, excellent performance can be guaranteed when the LDPC code istransmitted in the method as in the case of a small threshold value fromamong the plurality of cases for mapping. However, the method fordesigning the interleaver 120 based on the density evolution is atheoretical method. Therefore, the interleaver 120 may be designed byverifying the encoding performance based on a really designed paritycheck matrix and based on a cyclic distribution, in addition to thetheoretical method of density evolution.

Meanwhile, when the 180 bits groups are mapped onto the 10 bits, bitsgroups related to the rows having the same degree in the parity checkmatrix are grouped into a same group, and, onto which bits from amongthe 10 1024-QAM bits some of the groups in each group are mapped isdetermined.

For example, it is assumed that the parity check matrix of the LDPCcodeword includes rows having the degrees of 26, 3, and 2, and 14 bitgroups, 118 bit groups, and 36 bit groups are related to the rows havingthe degrees 26, 3, and 2, respectively,

In the case of the non-uniform 1024-QAM method, two bits have the samereceiving performance (that is, the same probability of reception) (thatis, P(y₀)=P(y₁), P(y₂)=P(y₃), P(y₄)=P(y₅), P(y₆)=P(y₇), P(y₈)=P(y₉)),and thus the bit groups may be mapped onto five (5) bits. Therefore, thenumber of cases where the bit groups are mapped onto the five (5) bitsmay be expressed as follows:

Number of cases modulated bits degree where bits are mapped y₀, y₁ 26 ₁₄C_(x1) y₂, y₃ 3 ₁₁₈C_(w1) 2   ₃₆C_(z1) 26  ₁₄C_(x2) 3 ₁₁₈C_(w2) 2₃₆C_(/7) y₄, y₅ 26  ₁₄C_(x3) 3 ₁₁₈C_(w3) 2   ₃₆C_(z3) y₆, y₇ 26 ₁₄C_(x4) 3 ₁₁₈C_(w4) 2   ₃₆C_(z4) y₈, y₉ 26  ₁₄C_(x5) 3 ₁₁₈C_(w5) 2  ₃₆C_(z5) sum 180

That is, regarding the bit groups to be mapped onto y₀ and y₁, thenumber of cases where x₁ number of bit groups are selected from amongthe bit groups related to the rows having the degree of 26, w₁ number ofbit groups are selected from among the bit groups related to the rowshaving the degree of three (3), and z₁ number of bit groups are selectedfrom among the bit groups related to the rows having the degree of two(2) may be ₁₄C_(x1)+₁₁₈C_(w1)+₃₆C_(z1).

In addition, regarding the bit groups to be mapped onto y₂ and y₃, thenumber of cases where x₂ number of bit groups are selected from amongthe bit groups related to the rows having the degree of 26, w₂ number ofbit groups are selected from among the bit groups related to the rowshaving the degree of three (3), and z₂ number of bit groups are selectedfrom among the bit groups related to the rows having the degree of two(2) may be ₁₄C_(x2)+₁₁₈C_(w2)+₃₆C_(z2).

In addition, regarding the bit groups to be mapped onto y₄ and y₅, thenumber of cases where x₃ number of bit groups are selected from amongthe bit groups related to the rows having the degree of 26, w₃ number ofbit groups are selected from among the bit groups related to the rowshaving the degree of three (3), and z₃ number of bit groups are selectedfrom among the bit groups related to the rows having the degree of two(2) may be ₁₄C_(x3)+₁₁₈C_(w3)+₃₆C_(z3).

In addition, regarding the bit groups to be mapped onto y₆ and y₇, thenumber of cases where x₄ number of bit groups are selected from amongthe bit groups related to the rows having the degree of 26, w₄ number ofbit groups are selected from among the bit groups related to the rowshaving the degree of three (3), and z₄ number of bit groups are selectedfrom among the bit groups related to the rows having the degree of two(2) may be ₁₄C_(x4)+₁₁₈C_(w4)+₃₆C_(z4).

In addition, regarding the bit groups to be mapped onto y₈ and y₉, thenumber of cases where x₅ number of bit groups are selected from amongthe bit groups related to the rows having the degree of 26, w₅ number ofbit groups are selected from among the bit groups related to the rowshaving the degree of three (3), and z₅ number of bit groups are selectedfrom among the bit groups related to the rows having the degree of two(2) may be ₁₄C_(x5)+₁₁₈C_(w5)+₃₆C_(z5).

In this case, x₁+x₂+x₃+x₄+x₅=14, w₁+w₂+w₃+w₄+W₅=118, andz₁+z₂+z₃+z₄+z₅=36.

However, since there are a large number of cases in the above example,it may be difficult to estimate performance for each case throughdensity evolution.

Therefore, the number of cases may be calculated by reducing the numberof kinds of receiving performance, and then performance for each casemay be estimated through density evolution.

For example, on the assumption that the probability of reception of y₀,y₁, y₂, and y₃ is the same and the probability of reception of y₄, y₅,y₆, y₇, y₈, and y₉ is the same as shown in a table presented below, thenumber of cases where the bit groups are mapped onto three (3) bits maybe calculated.

Number of cases modulated bits degree where bits are mapped y₀, y₁, y₂,y₃ 26 ₁₄C_(x1) 3 ₁₁₈C_(w1 ) 2 ₃₆C_(z1) y₄ y₅, y₆, y₇, y₈, y₉ 26 ₁₄C_(x2)3 ₁₁₈C_(w2 ) 2 ₃₆C_(z2) sum 180

That is, regarding the bit groups to be mapped onto y₀, y₁, y₂, y₃, thenumber of cases where x₁ number of bit groups are selected from amongthe bit groups related to the rows having the degree of 26, w₁ number ofbit groups are selected from among the bit groups related to the rowshaving the degree of three (3), and z₁ number of bit groups are selectedfrom among the bit groups related to the rows having the degree of two(2) may be ₁₄C_(x1)+₁₁₈C_(w1)+36C_(z1).

In addition, regarding the bit groups to be mapped onto y₄, y₅, y₆, y₇,y₈, y₉, the number of cases where x₂ number of bit groups are selectedfrom among the bit groups related to the rows having the degree of 26,w₂ number of bit groups are selected from among the bit groups relatedto the rows having the degree of three (3), and z₂ number of bit groupsare selected from among the bit groups related to the rows having thedegree of two (2) may be ₁₄C_(x2)+₁₁₈C_(w2)+₃₆C_(z2).

In this case, x₁+x₂=14, w₁+w₂=118, and z₁+z₂=36.

Thereafter, after the performance for each case is estimated throughdensity devolution, the case which is estimated to have the bestperformance is selected. That is, how many bit groups should be selectedfrom each of the bit groups related to the rows having the degrees of26, 3, and 2 and mapped onto y₀, y₁, y₂, y₃, and y₄, y₅, y₆, y₇, y₈, y₉in order to have the best performance is determined through densityevolution, and x₁, x₂, w₁, w₁, z¹, z² are determined.

Thereafter, the bits which are assumed to have the same receivingperformance are determined to have different receiving performance, andthe above-described process is repeated.

That is, the number of cases where the bit groups are mapped onto y₀,y₁, y₂, y₃ within x₁, w₁, z₁ is calculated based on determined x₁, w₁,z₁, and performance for each case is estimated through density evolutionand the case which is estimated to have the best performance isselected.

In addition, the number of cases where the bit groups are mapped ontoy₄, y₅, y₆, y₇, y₈, y₉ within x₂, w₂, z₂ is calculated based ondetermined x₂, w₂, z₂, and performance for each case is estimatedthrough density evolution and the case which is estimated to have thebest performance is selected.

Accordingly, how many of the bit groups related to the rows having eachof the degrees should be mapped onto the 1024-QAM bits to have the bestperformance may be determined, and the interleaver 120 may be designedto be able to map a specific group of the LDPC codeword onto a specificbit of the modulation symbol and satisfy the case of the bestperformance.

In the above-described method, the group interleaving method can bedesigned.

The transmitting apparatus 200 may transmit the signal mapped onto theconstellation to a receiving apparatus (for example, 2700 of FIG. 18 ).For example, the transmitting apparatus 200 may map the signal mappedonto the constellation onto an Orthogonal Frequency DivisionMultiplexing (OFDM) frame using OFDM, and may transmit the signal to thereceiving apparatus 2700 through an allocated channel.

Exemplary Embodiment 2: Case in which a Block-Row Interleaver is Used

According to another exemplary embodiment, the interleaver 120 mayinterleave an LDPC codeword in other methods, different from the methodsdescribed in above Exemplary Embodiment 1, and may map bits included ina predetermined bit group from among a plurality of bit groupsconstituting the interleaved LDPC codeword onto a predetermined bit of amodulation symbol. This will be explained in detail with reference toFIG. 14 .

Referring to FIG. 14 , the interleaver 120 includes a parity interleaver121, a group interleaver (or a group-wise interleaver 122), a grouptwist interleaver 123 and a block-row interleaver 125. Herein, theparity interleaver 121 and the group twist interleaver 123 perform thesame functions as in Exemplary Embodiment 1 described above, and thus, adetailed description of these elements is omitted.

The group interleaver 122 may divide a parity-interleaved LDPC codewordinto a plurality of bit groups, and may rearrange the order of theplurality of bit groups in bits group wise.

In this case, the operation of dividing the parity-interleaved LDPCcodeword into the plurality of bit groups is the same as in ExemplaryEmbodiment 1, and thus, a detailed description thereof is omitted.

The group interleaver 122 interleaves the LDPC codeword in bits groupwise. Specifically, the group interleaver 122 may group the LDPCcodeword into the plurality of bit groups, and may rearrange theplurality of bit groups in bits group wise. That is, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin the LDPC codeword in group units by changing locations of theplurality of bit groups constituting the LDPC codeword.

Herein, the group interleaver 122 may rearrange the order of theplurality of bit groups in bits group wise such that bit groupsincluding bits mapped onto the same modulation symbol from among theplurality of bit groups are serially arranged.

In this case, the group interleaver 122 may rearrange the order of theplurality of bit groups in bits group wise by considering at least oneof the number of rows and columns of the block-row interleaver 124, thenumber of bit groups of the LDPC codeword, and the number of bitsincluded in each bit group, such that bit groups including bits mappedonto the same modulation symbol are serially arranged.

To achieve this, the group interleaver 122 may interleave the LDPCcodeword in bits group wise by using Equation 17 presented below:Y _(j) =x _(π(j))(0≤j<N _(group))  (17),where X_(j) is the j^(th) bit group before group interleaving, and Y_(j)is the j^(th) bit group after group interleaving. In addition, π(j) is aparameter indicating an interleaving order and is determined by at leastone of a length of an LDPC codeword, a code rate, and a modulationmethod.

Accordingly, X_(π(j)) is a π(j)^(th) bit group before groupinterleaving, and Equation 17 means that the pre-interleaving π(j)^(th)bit group is interleaved into the j^(th) bit group.

According to an exemplary embodiment, an example of π(j) may be definedas in Tables 29 to 33 presented below.

In this case, π(j) is defined according to a length of an LPDC codewordand a code rate, and a parity check matrix is also defined according toa length of an LDPC codeword and a code rate. Accordingly, when LDPCencoding is performed based on a specific parity check matrix accordingto a length of an LDPC codeword and a code rate, the LDPC codeword maybe interleaved in bits group wise based on π(j) satisfying thecorresponding length of the LDPC codeword and code rate.

For example, when the encoder 110 performs LDPC encoding at a code rateof 6/15 to generate an LDPC codeword of a length of 64800, the groupinterleaver 122 may perform interleaving by using π(j) which is definedaccording to the length of the LDPC codeword of 64800 and the code rateof 6/15 in Tables 29 to 33 presented below, for example, by using π(j)defined as shown in Table 29.

For example, when the length N_(ldpc) of the LDPC codeword is 64800, thecode rate is 6/15, and the modulation method is 1024-QAM, π(j) may bedefined as in Table 29 presented below.

TABLE 29 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 66 59 22 15 106 97 74 88 132 134 21 14 block of 148 76 143 16693 174 95 55 42 38 9 131 Group-wise 5 94 168 164 24 56 19 45 138 96 119140 interleaver 120 12 43 18 152 130 78 144 6 118 110 70 input, 41 49167 86 90 157 147 114 47 67 25 27 16 156 85 160 72 145 68 136 60 113 162100 115 171 0 39 36 48 92 111 83 146 89 176 69 126 28 124 172 159 73 102116 71 1 177 Order of bits group to be block interleaved π(j) (0 ≤ j <180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 3738 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 31 37127 149 142 87 125 82 51 40 161 block of 81 7 103 169 133 54 62 30 13105 32 Group-wise 79 154 33 2 17 46 75 3 20 165 84 interleaver 64 4 50101 107 151 137 179 170 63 58 input, 117 98 11 10 91 153 65 53 44 77 173141 163 109 8 61 29 35 108 150 175 129 57 52 26 178 135 158 155 122 8099 23 34 121 139 128 112 104 123

In the case of Table 29, Equation 17 may be expressed asY₀=X_(π(0))=X₆₆, Y₁=X_(π(1))=X₅₉, Y₂=X_(π(2))=X₂₂, . . . ,Y₁₇₈=X_(π(178))=X₁₀₄, and Y₁₇₉=X_(π(179))=X₁₂₃. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 66^(th) bit group to the 0^(th) bitgroup, the 59^(th) bit group to the 1^(st) bit group, the 22^(nd) bitgroup to the 2^(nd) bit group, . . . , the 104^(th) bit group to the178^(th) bit group, and the 123^(rd) bit group to the 179^(th) bitgroup.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 8/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 30 presented below.

TABLE 30 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 77 39 3 175 102 62 119 0 171 104 48 13 block of 68 112 28 168167 106 135 51 75 54 85 122 Group-wise 120 107 150 100 69 18 145 15 2924 114 117 interleaver 170 6 89 78 74 105 21 159 177 162 156 71 input,63 66 101 98 179 164 111 5 84 36 87 37 95 161 11 133 154 50 47 86 4 13722 130 134 140 61 42 1 16 131 103 172 129 146 116 70 17 46 59 113 124176 132 7 73 56 14 Order of bits group to be block interleaved π(j) (0 ≤j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 3637 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 72 91 30125 173 109 8 115 82 79 2 block of 26 118 128 144 121 57 41 52 94 110 45Group-wise 169 12 65 38 19 43 20 23 149 147 108 interleaver 49 80 60 138157 155 96 143 126 90 93 input, 174 35 160 152 141 127 81 64 67 92 33148 178 97 88 40 10 9 136 32 123 158 55 76 58 83 166 27 139 163 99 16553 44 34 31 153 151 142 25

In the case of Table 30, Equation 17 may be expressed asY₀=X_(π(0))=X₇₇, Y₁=X_(π(1))=X₃₉, Y₂=X_(π(2))=X₃, . . . ,Y₁₇₈=X_(π(178))=X₁₄₂, and Y₁₇₉=X_(π(179))=X₂₅. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 77^(th) bit group to the 0^(th) bitgroup, the 39^(th) bit group to the 1^(st) bit group, the 3^(rd) bitgroup to the 2^(nd) bit group, . . . , the 142^(th) bit group to the178^(th) bit group, and the 25^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 10/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 31 presented below.

TABLE 31 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 7 87 5 66 23 42 149 43 148 16 58 9 block of 25 35 41 173 123 1673 59 81 116 39 72 Group-wise 132 130 164 169 14 71 75 53 98 21 170 127interleaver 156 115 50 47 112 38 117 69 157 138 120 57 input, 99 83 6362 133 177 6 19 64 52 103 22 11 160 151 124 158 8 100 105 51 48 67 128174 152 113 111 107 85 96 49 84 18 131 141 89 95 45 26 56 162 137 165125 104 92 28 Order of bits group to be block interleaved π(j) (0 ≤ j <180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 3738 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 82 10279 12 163 135 147 172 108 93 10 block of 97 159 178 136 155 1 94 109 7833 2 Group-wise 146 142 54 106 91 118 40 61 179 145 153 interleaver 4480 0 24 70 139 176 161 122 29 15 input, 73 34 154 140 143 144 65 4 30 3620 134 17 13 101 90 76 55 27 37 168 126 60 77 88 86 68 114 171 129 175166 46 119 110 32 31 74 150 121

In the case of Table 31, Equation 17 may be expressed as Y₀=X_(π(0))=X₇,Y₁=X_(π(1))=X₈₇, Y₂=X_(π(2))=X₅, . . . , Y₁₇₈=X_(π(178))=X₁₅₀, andY₁₇₉=X_(π(179))=X₁₂₁. Accordingly, the group interleaver 122 mayrearrange the order of the plurality of bit groups in bits group wise bychanging the 7^(th) bit group to the 0^(th) bit group, the 87^(th) bitgroup to the 1^(st) bit group, the 5^(th) bit group to the 2^(nd) bitgroup, . . . , the 150^(th) bit group to the 178^(th) bit group, and the121^(st) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 10/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 32 presented below.

TABLE 32 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 111 32 70 77 54 93 122 65 165 144 45 101 block of 117 60 42 131177 148 11 97 23 10 20 114 Group-wise 154 139 163 134 63 68 99 106 105119 6 167 interleaver 130 15 31 73 102 103 21 142 176 143 146 9 input,12 113 80 76 136 89 132 145 39 110 1 72 28 162 168 147 129 24 58 61 11591 34 123 155 125 100 87 90 30 46 86 150 170 149 5 62 14 29 33 92 174127 158 18 41 85 47 Order of bits group to be block interleaved π(j) (0≤ j < 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 3536 37 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 6768 output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 95 238 7 126 13 156 128 78 82 57 block of 51 160 166 179 175 75 79 50 74 5940 Group-wise 3 124 35 98 118 83 67 8 22 172 133 interleaver 107 27 1090 81 141 153 121 161 25 19 input, 64 112 157 152 169 120 94 48 17 88 4135 173 164 84 71 55 37 66 36 159 52 49 43 56 116 108 69 171 138 178 15144 26 104 53 137 96 16 140

In the case of Table 32, Equation 17 may be expressed asY₀=X_(π(0))=X₁₁₁, Y₁=X_(π(1))=X₃₂, Y₂=X_(π(2))=X₇₀, . . . ,Y₁₇₈=X_(π(178))=X₁₆, and Y₁₇₉=X_(π(179))=X₁₄₀. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 111^(th) bit group to the 0^(th) bitgroup, the 32^(nd) bit group to the 1^(st) bit group, the 70^(th) bitgroup to the 2^(nd) bit group, . . . , the 16^(th) bit group to the178^(th) bit group, and the 140^(th) bit group to the 179^(th) bitgroup.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 12/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 33 presented below.

TABLE 33 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 output 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 91 88 112 102 26 27 120 103 17 15 19 136 block of 64 98 29 126164 167 5 106 121 73 86 37 Group-wise 149 54 179 163 40 133 92 39 44 13974 166 interleaver 175 67 2 48 125 25 109 178 123 160 151 32 input, 110119 34 59 18 0 161 176 31 38 80 6 142 42 10 156 153 78 69 138 35 128 96165 24 158 79 81 85 71 84 99 134 162 170 168 58 130 45 28 13 140 66 1598 95 46 57 Order of bits group to be block interleaved π(j) (0 ≤ j <180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 3738 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68output 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 60 83116 89 115 72 147 148 11 52 33 block of 62 143 93 174 146 14 1 53 100 5550 Group-wise 3 172 20 4 75 49 70 56 41 43 173 interleaver 21 47 108 777 129 113 155 169 22 122 input, 114 127 131 154 152 150 23 12 76 118135 63 177 171 68 111 87 61 137 105 101 107 141 82 65 30 51 90 36 157 9144 117 94 97 124 132 104 16 145

In the case of Table 33, Equation 17 may be expressed asY₀=X_(π(0))=X₉₁, Y₁=X_(π(1))=X₈₈, Y₂=X_(π(2))=X₁₁₂, . . . ,Y₁₇₈=X_(π(178))=X₁₆, and Y₁₇₉=X_(π(179))=X₁₄₅. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 91^(st) bit group to the 0^(th) bitgroup, the 88^(th) bit group to the 1^(st) bit group, the 112^(th) bitgroup to the 2^(nd) bit group, . . . , the 16^(th) bit group to the178^(th) bit group, and the 145^(th) bit group to the 179^(th) bitgroup.

In the above-described examples, the length of the LDPC codeword is64800 and the code rate is 6/15, 8/15, 10/15, and 12/15. However, thisis merely an example and the interleaving pattern may be definedvariously when the length of the LDPC codeword is 16200 or the code ratehas different values.

As described above, the group interleaver 122 may rearrange the order ofthe plurality of bit groups in bits group wise by using Equation 17 andTables 29 to 33.

“j-th block of Group-wise Interleaver output” in Tables 29 to 33indicates the j-th bit group output from the group interleaver 122 afterinterleaving, and “π(j)-th block of Group-wise Interleaver input”indicates the π(j)-th bit group input to the group interleaver 122.

In addition, since the order of the bit groups constituting the LDPCcodeword is rearranged by the group interleaver 122 in bits group wise,and then the bit groups are block-interleaved by the block interleaver124, which will be described below, “Order of bits groups to be blockinterleaved” is set forth in Tables 29 to 33 in relation to π(j).

π(j) defined as shown in Tables 29 to 33 may be arranged according tothe code rates as shown in Table 34 presented below:

TABLE 34 (CR 6/15) (CR 8/15) (CR 10/15) (CR 10/15) (CR 12/15) j-th blockof π(j)-th block of π(j)-th block of π(j)-th block of π(j)-th block ofπ(j)-th block of Group-wise Group-wise Group-wise Group-wise Group-wiseGroup-wise Interleaver Interleaver Interleaver Interleaver InterleaverInterleaver output input input input input input 0 66 77 7 111 91 1 5939 87 32 88 2 22 3 5 70 112 3 15 175 66 77 102 4 106 102 23 54 26 5 9762 42 93 27 6 74 119 149 122 120 7 88 0 43 65 103 8 132 171 148 165 17 9134 104 16 144 15 10 21 48 58 45 19 11 14 13 9 101 136 12 31 72 82 95 6013 37 91 102 2 83 14 127 30 79 38 116 15 149 125 12 7 89 16 142 173 163126 115 17 87 109 135 13 72 18 125 8 147 156 147 19 82 115 172 128 14820 51 82 108 78 11 21 40 79 93 82 52 22 161 2 10 57 33 23 148 68 25 11764 24 76 112 35 60 98 25 143 28 41 42 29 26 166 168 173 131 126 27 93167 123 177 164 28 174 106 167 148 167 29 95 135 3 11 5 30 55 51 59 97106 31 42 75 81 23 121 32 38 54 116 10 73 33 9 85 39 20 86 34 131 122 72114 37 35 81 26 97 51 62 36 7 118 159 160 143 37 103 128 178 166 93 38169 144 136 179 174 39 133 121 155 175 146 40 54 57 1 75 14 41 62 41 9479 1 42 30 52 109 50 53 43 13 94 78 74 100 44 105 110 33 59 55 45 32 452 40 50 46 5 120 132 154 149 47 94 107 130 139 54 48 168 150 164 163 17949 164 100 169 134 163 50 24 69 14 63 40 51 56 18 71 68 133 52 19 145 7599 92 53 45 15 53 106 39 54 138 29 98 105 44 55 96 24 21 119 139 56 119114 170 6 74 57 140 117 127 167 166 58 79 169 146 3 3 59 154 12 142 124172 60 33 65 54 35 20 61 2 38 106 98 4 62 17 19 91 118 75 63 46 43 11883 49 64 75 20 40 67 70 65 3 23 61 8 56 66 20 149 179 22 41 67 165 147145 172 43 68 84 108 153 133 173 69 120 170 156 130 175 70 12 6 115 1567 71 43 89 50 31 2 72 18 78 47 73 48 73 152 74 112 102 125 74 130 10538 103 25 75 78 21 117 21 109 76 144 159 69 142 178 77 6 177 157 176 12378 118 162 138 143 160 79 110 156 120 146 151 80 70 71 57 9 32 81 64 4944 107 21 82 4 80 80 27 47 83 50 60 0 109 108 84 101 138 24 0 7 85 107157 70 81 77 86 151 155 139 141 129 87 137 96 176 153 113 88 179 143 161121 155 89 170 126 122 161 169 90 63 90 29 25 22 91 58 93 15 19 122 9241 63 99 12 110 93 49 66 83 113 119 94 167 101 63 80 34 95 86 98 62 7659 96 90 179 133 136 18 97 157 164 177 89 0 98 147 111 6 132 161 99 1145 19 145 176 100 47 84 64 39 31 101 67 36 52 110 38 102 25 87 103 1 80103 27 37 22 72 6 104 117 174 73 64 114 105 98 35 34 112 127 106 11 160154 157 131 107 10 152 140 152 154 108 91 141 143 169 152 109 153 127144 120 150 110 65 81 65 94 23 111 53 64 4 48 12 112 44 67 30 17 76 11377 92 36 88 118 114 173 33 20 4 135 115 16 95 11 28 142 116 156 161 160162 42 117 85 11 151 168 10 118 160 133 124 147 156 119 72 154 158 129153 120 145 50 8 24 78 121 68 47 100 58 69 122 136 86 105 61 138 123 604 51 115 35 124 113 137 48 91 128 125 162 22 67 34 96 126 100 130 128123 165 127 141 148 134 135 63 128 163 178 17 173 177 129 109 97 13 164171 130 8 88 101 84 68 131 61 40 90 71 111 132 29 10 76 55 87 133 35 955 37 61 134 108 136 27 66 137 135 150 32 37 36 105 136 175 123 168 159101 137 129 158 126 52 107 138 115 134 174 155 24 139 171 140 152 125158 140 0 61 113 100 79 141 39 42 111 87 81 142 36 1 107 90 85 143 48 1685 30 71 144 92 131 96 46 84 145 111 103 49 86 99 146 83 172 84 150 134147 146 129 18 170 162 148 89 146 131 149 170 149 176 116 141 5 168 15057 55 60 49 141 151 52 76 77 43 82 152 26 58 88 56 65 153 178 83 86 11630 154 135 166 68 108 51 155 158 27 114 69 90 156 155 139 171 171 36 157122 163 129 138 157 158 80 99 175 178 9 159 99 165 166 151 144 160 23 5346 44 117 161 69 70 89 62 58 162 126 17 95 14 130 163 28 46 45 29 45 164124 59 26 33 28 165 172 113 56 92 13 166 159 124 162 174 140 167 73 176137 127 66 168 102 132 165 158 159 169 116 7 125 18 8 170 71 73 104 4195 171 1 56 92 85 46 172 177 14 28 47 57 173 34 44 119 26 94 174 121 34110 104 97 175 139 31 32 53 124 176 128 153 31 137 132 177 112 151 74 96104 178 104 142 150 16 16 179 123 25 121 140 145

“j-th block of Group-wise Interleaver output” in Table 34 indicates thej-th bit group output from the group interleaver 122 after interleaving,and “π(j)-th block of Group-wise Interleaver input” indicates theπ(j)-th bit group input to the group interleaver 122. Referring to Table34, it can be seen that Table 34 is the arrangements of data describedin Tables 29 to 33 according to the code rates.

The group interleaver 122 may interleave the LDPC codeword in bits groupwise by using Equation 18 presented below:Y _(π(j)) =X _(j)(0≤j<N _(group))  (18),where X_(j) is the j^(th) bit group before group interleaving, and Y_(j)is the j^(th) bit group after group interleaving. In addition, π(j) is aparameter indicating an interleaving order and is determined by at leastone of a length of an LDPC codeword, a code rate, and a modulationmethod.

Accordingly, X_(j) is a j^(th) bit group before group interleaving, andEquation 18 means that the pre-interleaving j^(th) bit group isinterleaved into the π(j)^(th) bit group.

According to an exemplary embodiment, an example of π(j) may be definedas in Tables 35 to 39 presented below.

In this case, π(j) is defined according to a length of an LPDC codewordand a code rate, and a parity check matrix is also defined according toa length of an LDPC codeword and a code rate. Accordingly, when LDPCencoding is performed based on a specific parity check matrix accordingto a length of an LDPC codeword and a code rate, the LDPC codeword maybe interleaved in bits group wise based on π(j) satisfying thecorresponding length of the LDPC codeword and code rate.

For example, when the encoder 110 performs LDPC encoding at a code rateof 6/15 to generate an LDPC codeword of a length of 64800, the groupinterleaver 122 may perform interleaving by using π(j) which is definedaccording to the length of the LDPC codeword of 64800 and the code rateof 6/15 in Tables 35 to 39 presented below, for example, by using π(j)defined as shown in Table 35.

For example, when the length N_(ldpc) of the LDPC codeword is 64800, thecode rate is 6/15, and the modulation method is 1024-QAM, π(j) may bedefined as in Table 35 presented below.

TABLE 35 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 140 171 61 65 82 46 77 36 130 33 107 106 block of 160 50 102 152103 163 132 42 12 45 60 173 Group-wise 63 100 143 93 83 20 151 111 40 3051 150 interleaver 161 80 170 119 167 6 64 24 113 75 58 158 output, 14427 47 29 55 5 105 159 126 84 168 37 138 169 104 78 56 69 174 157 179 16418 162 54 175 57 127 16 25 76 120 147 98 23 15 22 125 128 49 67 26 94 4838 89 139 165 Order of bits group to be block interleaved π(j) (0 ≤ j <180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 3738 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 70 43 113 115 62 72 52 66 10 2 block of 133 142 143 32 141 21 92 31 71 112 53Group-wise 91 1 123 131 41 90 81 110 0 101 121 interleaver 35 19 146 68117 95 17 7 148 96 108 output, 178 44 4 85 134 129 79 145 177 124 99 14176 137 74 34 8 39 9 154 122 87 135 86 73 109 59 156 116 97 155 166 118114 28 136 149 172 153 88

In the case of Table 35, Equation 18 may be expressed asX₀=Y_(π(0))=Y₁₄₀, X₁=Y_(π(1))=Y₁₇₁, X₂=Y_(π(2))=Y₆₁, . . . ,X₁₇₈=Y_(π(178))=Y₁₅₃, and X₁₇₉=Y_(π(179))=Y₈₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 0^(th) bit group to the 140^(th) bitgroup, the 1^(st) bit group to the 171^(st) bit group, the 2^(nd) bitgroup to the 61^(st) bit group, . . . , the 178^(th) bit group to the153^(rd) bit group, and the 179^(th) bit group to the 88^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 8/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 36 presented below.

TABLE 36 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 7 142 22 2 123 99 70 169 18 133 132 117 block of 65 55 179 35155 25 54 14 175 135 114 174 Group-wise 163 121 10 81 120 30 42 160 32150 171 40 interleaver 50 161 80 12 170 73 31 151 0 72 21 82 output, 11391 43 115 87 129 95 158 49 94 4 145 19 149 57 36 6 46 39 34 136 166 1589 84 156 139 108 178 88 38 52 148 67 127 66 116 78 157 97 159 154 27 2658 69 8 146 Order of bits group to be block interleaved π(j) (0 ≤ j <180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 3738 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 59 11172 53 143 162 51 62 64 75 125 block of 105 101 103 61 1 131 41 141 63173 45 Group-wise 152 164 83 140 5 92 111 60 93 112 23 interleaver 11020 153 100 33 122 102 130 71 90 13 output, 9 74 28 47 68 17 44 98 24 16556 109 37 147 126 144 168 118 138 29 134 124 48 177 107 176 119 86 79 85137 76 106 16 104 3 167 77 128 98

In the case of Table 36, Equation 18 may be expressed as X₀=Y_(π(0))=Y₇,X₁=Y_(π(1))=Y₁₄₂, X₂=Y_(π(2))=Y₂₂, . . . , X₁₇₈=Y_(π(178))=Y₁₂₈, andX₁₇₉=Y_(π(179))=Y₉₈. Accordingly, the group interleaver 122 mayrearrange the order of the plurality of bit groups in bits group wise bychanging the 0^(th) bit group to the 7^(th) bit group, the 1^(st) bitgroup to the 142^(nd) bit group, the 2^(nd) bit group to the 22^(nd) bitgroup, . . . , the 178^(th) bit group to the 128^(th) bit group, and the179^(th) bit group to the 98^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 10/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 37 presented below.

TABLE 37 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 83 40 45 29 111 2 98 0 120 11 22 115 block of 4 84 23 164 134172 90 112 176 175 44 105 Group-wise 160 72 124 145 71 123 101 53 60 133165 80 interleaver 76 85 51 34 104 177 52 132 151 43 14 82 output, 17121 41 162 144 35 54 92 121 130 13 102 70 32 75 63 173 79 179 89 27 118169 137 78 86 107 149 59 108 109 67 58 18 8 6 88 166 16 48 168 159 28136 49 56 156 19 Order of bits group to be block interleaved π(j) (0 ≤ j< 180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 3637 38 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 15 12950 91 9 128 147 99 114 55 103 block of 24 113 135 74 33 64 25 5 7 81 163Group-wise 10 30 150 65 95 94 100 110 3 125 154 interleaver 31 12 93 146143 153 1 152 161 131 62 output, 170 122 61 142 20 42 174 141 73 140 15557 126 157 47 148 46 96 127 17 38 167 178 117 139 68 106 39 69 77 119 36116 26 138 158 87 97 37 66

In the case of Table 37, Equation 18 may be expressed asX₀=Y_(π(0))=Y₈₃, X₁=Y_(π(1))=Y₄₀, X₂=Y_(π(2))=Y₄₅, . . . ,X₁₇₈=Y_(π(178))=Y₃₇, and X₁₇₉=Y_(π(179))=Y₆₆. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 0^(th) bit group to the 83^(rd) bitgroup, the 1^(st) bit group to the 40^(th) bit group, the 2^(nd) bitgroup to the 45^(th) bit group, . . . , the 178^(th) bit group to the37^(th) bit group, and the 179^(th) bit group to the 66^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 10/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 38 presented below.

TABLE 38 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 84 102 13 58 114 149 56 15 65 80 32 29 block of 31 120 90 173 82115 163 143 71 1 164 125 Group-wise 144 172 111 150 42 35 137 175 4 132152 22 interleaver 155 2 131 103 72 43 40 95 3 20 41 94 output, 165 5110 12 177 30 61 52 140 11 73 74 123 153 23 62 55 109 88 6 126 59 139 16157 47 179 86 76 78 9 99 79 118 28 148 89 116 48 129 8 37 57 117 108 147156 67 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 37 38 3940 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68 input 8182 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 92 17 162 70 178112 169 91 33 75 66 block of 60 135 133 14 100 45 170 25 151 160 10Group-wise 121 44 24 122 161 50 104 7 134 64 51 interleaver 85 21 63 130171 145 141 113 97 142 124 output, 174 54 53 81 154 83 101 0 105 93 34167 19 119 69 26 98 68 49 127 96 176 146 159 107 87 46 138 18 106 168136 36 128 166 39 77 27 158 38

In the case of Table 38, Equation 18 may be expressed asX₀=Y_(π(0))=Y₈₄, X₁=Y_(π(1))=Y₁₀₂, X₂=Y_(π(2))=Y₁₃, . . . ,X₁₇₈=Y_(π(178))=Y₁₅₈, and X₁₇₉=Y_(π(179))=Y₃₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 0^(th) bit group to the 84^(th) bitgroup, the 1^(st) bit group to the 102^(th) bit group, the 2^(nd) bitgroup to the 13^(th) bit group, . . . , the 178^(th) bit group to the158^(th) bit group, and the 179^(th) bit group to the 38^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 12/15, and the modulation method is 1024-QAM,π(j) may be defined as in Table 39 presented below.

TABLE 39 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 Group-wise 23 24 25 26 27 28 2930 31 32 33 34 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 input 6970 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172π(j)-th 97 41 71 58 61 29 103 84 169 158 117 20 block of 110 138 74 4 5164 25 153 100 80 22 94 Group-wise 171 82 72 63 45 154 21 42 47 44 65172 interleaver 121 64 143 17 32 56 62 112 85 120 140 102 output, 52 37173 170 125 174 24 145 43 136 3 7 16 14 160 113 93 6 31 91 77 175 73 26122 55 166 150 115 36 159 179 39 18 19 46 98 147 49 27 126 57 28 149 89148 129 59 Order of bits group to be block interleaved π(j) (0 ≤ j <180) j-th block of 12 13 14 15 16 17 18 19 20 21 22 Group-wise 35 36 3738 39 40 41 42 43 44 45 interleaver 58 59 60 61 62 63 64 65 66 67 68input 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j)-th 111 16540 9 178 8 96 10 60 81 90 block of 123 156 34 101 53 50 66 116 67 54 163Group-wise 161 95 12 133 35 127 23 152 167 70 130 interleaver 141 151 13144 142 33 132 1 15 155 0 output, 177 135 30 137 83 75 92 131 2 87 104105 124 86 162 106 176 51 146 114 11 134 109 79 108 119 107 88 118 157139 168 78 68 38 69 99 128 76 48

In the case of Table 39, Equation 18 may be expressed asX₀=Y_(π(0))=Y₉₇, X₁=Y_(π(1))=Y₄₁, X₂=Y_(π(2))=Y₇₁, . . . ,X₁₇₈=Y_(π(178))=Y₇₆, and X₁₇₉=Y_(π(179))=Y₄₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bits group wise by changing the 0^(th) bit group to the 97^(th) bitgroup, the 1^(st) bit group to the 41^(st) bit group, the 2^(nd) bitgroup to the 71^(st) bit group, . . . , the 178^(th) bit group to the76^(th) bit group, and the 179^(th) bit group to the 48^(th) bit group.

In the above-described examples, the length of the LDPC codeword is64800 and the code rate is 6/15, 8/15, 10/15, and 12/15. However, thisis merely an example and the interleaving pattern may be definedvariously when the length of the LDPC codeword is 16200 or the code ratehas different values.

As described above, the group interleaver 122 may rearrange the order ofthe plurality of bit groups in bits group wise by using Equation 18 andTables 35 to 39.

“j-th block of Group-wise Interleaver input” in Tables 35 to 39indicates the j-th bit group input to the group interleaver 122 beforeinterleaving, and “π(j)-th block of Group-wise Interleaver output”indicates the π(j)-th bit group output from the group interleaver 122after interleaving.

In addition, since the order of the bit groups constituting the LDPCcodeword is rearranged by the group interleaver 122 in bits group wise,and then the bit groups are block-interleaved by the block interleaver124, which will be described below, “Order of bits groups to be blockinterleaved” is set forth in Tables 35 to 39 in relation to π(j).

π(j) defined as shown in Tables 35 to 39 may be arranged according tothe code rates as shown in Table 40:

TABLE 40 (CR 6/15) (CR 8/15) (CR 10/15) (CR 10/15) (CR 12/15) j-th blockof □(j)-th block of □(j)-th block of □(j)-th block of □(j)-th block of□(j)-th block of Group-wise Group-wise Group-wise Group-wise Group-wiseGroup-wise Interleaver Interleaver Interleaver Interleaver InterleaverInterleaver input output output output output output 0 140 7 83 84 97 1171 142 40 102 41 2 61 22 45 13 71 3 65 2 29 58 58 4 82 123 111 114 61 546 99 2 149 29 6 77 70 98 56 103 7 36 169 0 15 84 8 130 18 120 65 169 933 133 11 80 158 10 107 132 22 32 117 11 106 117 115 29 20 12 70 59 1592 111 13 43 11 129 17 165 14 11 172 50 162 40 15 3 53 91 70 9 16 115143 9 178 178 17 62 162 128 112 8 18 72 51 147 169 96 19 52 62 99 91 1020 66 64 114 33 60 21 10 75 55 75 81 22 2 125 103 66 90 23 160 65 4 31110 24 50 55 84 120 138 25 102 179 23 90 74 26 152 35 164 173 4 27 103155 134 82 5 28 163 25 172 115 164 29 132 54 90 163 25 30 42 14 112 143153 31 12 175 176 71 100 32 45 135 175 1 80 33 60 114 44 164 22 34 173174 105 125 94 35 133 105 24 60 123 36 142 101 113 135 156 37 13 103 135133 34 38 32 61 74 14 101 39 141 1 33 100 53 40 21 131 64 45 50 41 92 4125 170 66 42 31 141 5 25 116 43 71 63 7 151 67 44 112 173 81 160 54 4553 45 163 10 163 46 63 163 160 144 171 47 100 121 72 172 82 48 143 10124 111 72 49 93 81 145 150 63 50 83 120 71 42 45 51 20 30 123 35 154 52151 42 101 137 21 53 111 160 53 175 42 54 40 32 60 4 47 55 30 150 133132 44 56 51 171 165 152 65 57 150 40 80 22 172 58 91 152 10 121 161 591 164 30 44 95 60 123 83 150 24 12 61 131 140 65 122 133 62 41 5 95 16135 63 90 92 94 50 127 64 81 111 100 104 23 65 110 60 110 7 152 66 0 93 3134 167 67 101 112 125 64 70 68 121 23 154 51 130 69 161 50 76 155 12170 80 161 85 2 64 71 170 80 51 131 143 72 119 12 34 103 17 73 167 170104 72 32 74 6 73 177 43 56 75 64 31 52 40 62 76 24 151 132 95 112 77113 0 151 3 85 78 75 72 43 20 120 79 58 21 14 41 140 80 158 82 82 94 10281 35 110 31 85 141 82 19 20 12 21 151 83 146 153 93 63 13 84 68 100 146130 144 85 117 33 143 171 142 86 95 122 153 145 33 87 17 102 1 141 13288 7 130 152 113 1 89 148 71 161 97 15 90 96 90 131 142 155 91 108 13 62124 0 92 144 113 171 165 52 93 27 91 21 5 37 94 47 43 41 110 173 95 29115 162 12 170 96 55 87 144 177 125 97 5 129 35 30 174 98 105 95 54 6124 99 159 158 92 52 145 100 126 49 121 140 43 101 84 94 130 11 136 102168 4 13 73 3 103 37 145 102 74 7 104 178 9 170 174 177 105 44 74 122 54135 106 4 28 61 53 30 107 85 47 142 81 137 108 134 68 20 154 83 109 12917 42 83 75 110 79 44 174 101 92 111 145 98 141 0 131 112 177 24 73 1052 113 124 165 140 93 87 114 99 56 155 34 104 115 138 19 70 123 16 116169 149 32 153 14 117 104 57 75 23 160 118 78 36 63 62 113 119 56 6 17355 93 120 69 46 79 109 6 121 174 39 179 88 31 122 157 34 89 6 91 123 179136 27 126 77 124 164 166 118 59 175 125 18 15 169 139 73 126 162 89 13716 26 127 14 109 57 167 105 128 176 37 126 19 124 129 137 147 157 119 86130 74 126 47 69 162 131 34 144 148 26 106 132 8 168 46 98 176 133 39118 96 68 51 134 9 138 127 49 146 135 154 29 17 127 114 136 122 134 3896 11 137 87 124 167 176 134 138 54 84 78 157 122 139 175 156 86 47 55140 57 139 107 179 166 141 127 108 149 86 150 142 16 178 59 76 115 14325 88 108 78 36 144 76 38 109 9 159 145 120 52 67 99 179 146 147 148 5879 39 147 98 67 18 118 18 148 23 127 8 28 19 149 15 66 6 148 46 150 13548 178 146 109 151 86 177 117 159 79 152 73 107 139 107 108 153 109 17668 87 119 154 59 119 106 46 107 155 156 86 39 138 88 156 116 79 69 18118 157 97 85 77 106 157 158 155 137 119 168 139 159 166 76 36 136 168160 118 106 116 36 78 161 22 116 88 89 98 162 125 78 166 116 147 163 128157 16 48 49 164 49 97 48 129 27 165 67 159 168 8 126 166 26 154 159 3757 167 94 27 28 57 28 168 48 26 136 117 149 169 38 58 49 108 89 170 8969 56 147 148 171 139 8 156 156 129 172 165 146 19 67 59 173 114 16 26128 68 174 28 104 138 166 38 175 136 3 158 39 69 176 149 167 87 77 99177 172 77 97 27 128 178 153 128 37 158 76 179 88 96 66 38 48

Table 34 is the case in which group interleaving is performed usingEquation 17 and π(j) is applied as an index of an input bit group, andTable 40 is the case in which group interleaving is performed usingEquation 18 and π(j) is applied as an index of an output bit group.Therefore, Tables 34 and 40 have an inverse relationship with eachother.

As described above, the group interleaver 122 may rearrange the order ofthe plurality of bit groups in bits group wise by using Equation 18 andTables 35 to 39.

When the group interleaving is performed in the above-described method,the order of the bit groups constituting the group-interleaved LDPCcodeword is different from that of the bit groups of the LDPC codewordgroup-interleaved based on Tables 9 to 20.

This is because the block-row interleaver 125 is used instead of theblock interleaver 124 in the present exemplary embodiment. That is,since the interleaving method used in the block interleaver 124 and theinterleaving method used in the block-row interleaver 125 are differentfrom each other, the group interleaver 122 in the present exemplaryembodiment may rearrange the order of the plurality of bit groupsconstituting the LDPC codeword based on Tables 29 to 40.

Specifically, the group interleaver 122 may rearrange the order of theplurality of bit groups in bits group wise such that an arrangementunit, in which at least one bit group including bits to be mapped onto asame modulation symbol is serially arranged in bit group wise, isrepeated.

That is, the group interleaver 122 may serially arrange one of aplurality of first bit groups including bits to be mapped onto a firstspecific location of each modulation symbol, one of a plurality ofsecond bit groups including bits to be mapped onto a second specificlocation of each modulation symbol, . . . , one of a plurality of n^(th)bit groups including bits to be mapped onto an n^(th) specific locationof each modulation symbol, and may arrange the other bit groupsrepeatedly in the same method.

The block-row interleaver 125 interleaves the plurality of bit groupsthe order of which has been rearranged. In this case, the block-rowinterleaver 125 may interleave the plurality of bit groups the order ofwhich has been rearranged in bits group wise by using at least one rowincluding a plurality of columns. This will be explained in detail belowwith reference to FIGS. 15 to 17 .

FIGS. 15 to 17 are views to illustrate a configuration of a block-rowinterleaver and an interleaving method according to an exemplaryembodiment.

First, when N_(group)/m is an integer, the block-row interleaver 125includes an interleaver 125-1 including m number of rows each includingM number of columns as shown in FIG. 15 , and the block-row interleaver125 may interleave by using N_(group)/m number of interleavers 125-1having the configuration of FIG. 15 .

Herein, N_(group) is the total number of bit groups constituting an LDPCcodeword. In addition, M is the number of bits included in a single bitgroup and may be 360, for example. m may be equal to the number of bitsconstituting a modulation symbol or may be 1/2 of the number of bitsconstituting a modulation symbol. For example, when a non-uniform QAM isused, performance of the bits constituting the modulation symbol isdifferent, and thus, by setting m to be equal to the number of bitsconstituting the modulation symbol, a single bit group can be mappedonto a single bit of each modulation symbol.

Specifically, the block-row interleaver 125 may interleave by writingeach of the plurality of bit groups constituting the LDPC codeword ineach row in the row direction in bits group wise, and reading eachcolumn of the plurality of rows in which the plurality of bit groups arewritten in bit group wise in the column direction.

For example, as shown in FIG. 15 , the block-row interleaver 125 maywrite m number of continuous bit groups from among the plurality of bitgroups in each of the m number of rows of the interleaver 125-1 in therow direction, and read each column of m number of rows in which thebits are written in the column direction. In this case, as manyinterleavers 125-1 as the number of bit groups divided by the number ofrows, that is, N_(group)/m, may be used.

As described above, when the number of bit groups constituting the LDPCcodeword is an integer multiple of the number of rows, the block-rowinterleaver 125 may interleave by writing as many bit groups as thenumber of rows from among the plurality of bit groups serially.

On the other hand, when the number of bit groups constituting the LDPCcodeword is not an integer multiple of the number of rows, the block-rowinterleaver 125 may interleave by using N number of interleavers (N isan integer greater than or equal to 2) including a different number ofcolumns.

For example, as shown in FIGS. 16 and 17 , the block-row interleaver 125may interleave by using a first interleaver 125-2 including m number ofrows each including M number of columns, and a second interleaver 125-3including m number of rows each including a×M/m number of columns.Herein, a is N_(group)−└N_(group)/m┘×m, and └N_(group)/m┘ is the largestinteger below N_(group)/m.

In this case, the first interleaver 125-2 may be used as many as└N_(group)/m┘ and one second interleaver 125-3 may be used.

Specifically, the block-row interleaver 125 may interleave by writingeach of └N_(group)/m┘×m number of bit groups from among the plurality ofbit groups constituting the LDPC codeword in each row in the rowdirection in bits group wise, and reading each column of the pluralityof rows in which └N_(group)/m┘×m number of bit groups are written inbits group wise in the column direction.

For example, as shown in FIGS. 16 and 17 , the block-row interleaver 125may write the same m number of continuous bit groups as the number ofrows from among └N_(group)/m┘×M number of bit groups in each row of thefirst interleaver 125-2 in the row direction, and may read each columnof the plurality of rows of the first interleaver 125-2 in which mnumber of bit groups are written in the column direction. In this case,the first interleaver 125-2 having the configuration FIGS. 16 and 17 maybe used as many as └N_(group)/m┘.

Thereafter, the block-row interleaver 125 may divide the bits includedin bit groups other than the groups written in the first interleaver125-2, and may write these bits in each row of the second interleaver125-3 in the row direction. In this case, the same number of bits may bewritten in each row of the second interleaver 125-3.

For example, as shown in FIG. 16 , the block-row interleaver 125 maywrite, in each of m number of rows of the second interleaver 125-3,a×M/m number of bits from among the bits included in the other bitgroups, in the row direction, and may read each column of m number ofrows of the second interleaver 125-3 in which the bits are written inthe column direction. In this case, one second interleaver 125-3 havingthe configuration of FIG. 16 may be used.

However, according to another exemplary embodiment, as shown in FIG. 17, the block-row interleaver 125 may write the bits in the firstinterleaver 125-2 in the same method as explained in FIG. 16 , but maywrite the bits in the second interleaver 125-3 in a method differentfrom that of FIG. 16 .

That is, the block-row interleaver 125 may write the bits in the secondinterleaver 125-3 in the column direction.

For example, as shown in FIG. 17 , the block-row interleaver 125 maywrite the bits included in the bit groups other than the bit groupswritten in the first interleaver 125-2 in each column of m number ofrows each including a×M/m number of columns of the second interleaver125-3 in the column direction, and may read each column of m number ofrows of the second interleaver 125-3 in which the bits are written inthe column direction. In this case, one second interleaver 125-3 havingthe configuration of FIG. 17 may be used.

In the method shown in FIG. 17 , the block-row interleaver 125 mayinterleave by reading in the column direction after writing the bits inthe second interleaver in the column direction. Accordingly, the bitsincluded in the bit groups interleaved by the second interleaver areread in the order as they were written and output to the modulator 130.Accordingly, the bits included in the bit groups belonging to the secondinterleaver are not rearranged by the block-row interleaver 125 and maybe mapped onto the modulation symbols serially.

As described above, the block-row interleaver 125 may interleave theplurality of bit groups by using the methods described above withreference to FIGS. 15 to 17 .

According to the above-described method, the output of the block-rowinterleaver 125 may be the same as the output of the block interleaver124. Specifically, when the block-row interleaver 125 interleaves asshown in FIG. 15 , the block-row interleaver 125 may output the samevalue as that of the block interleaver 124 which interleaves as shown inFIG. 8 . In addition, when the block-row interleaver 125 interleaves asshown in FIG. 16 , the block-row interleaver 125 may output the samevalue as that of the block interleaver 124 which interleaves as shown inFIG. 9 . In addition, when the block-row interleaver 125 interleaves asshown in FIG. 17 , the block-row interleaver 125 may output the samevalue as that of the block interleaver 124 which interleaves as shown inFIG. 10 .

Specifically, when the group interleaver 122 is used based on Equation15 and the block interleaver 124 is used, and the output bit groups ofthe group interleaver 122 are Y_(i)(0≤j<N_(group)) and, when the groupinterleaver 122 is used based on Equation 17 and the block-rowinterleaver 125 is used, and the output groups of the group interleaver122 are Z_(i)(0≤j<N_(group)) a relationship between the output bitgroups Z_(i) and Y_(i) after group interleaving may be expressed as inEquations 19 and 20, and as a result, the same value may be output fromthe block interleaver 124:Z _(i+m×j) =Y _(α×i+j)(0≤i<m,0≤j<α)  (19)Z _(i) =Y _(i)(α×m≤i<N _(group))  (20)where a is └N_(group)/m┘ and is the number of bit groups input to asingle column of the first part when the block interleaver 124 is used,and └N_(group)/m┘ is the largest integer below N_(group)/m. Here, m maybe equal to the number of bits constituting the modulation symbol orhalf of the bits constituting the modulation symbol. In addition, m isthe number of columns of the block interleaver 124 and m is the numberof rows of the block-row interleaver 125.

The case in which group interleaving is performed by the groupinterleaver 122 based on Equation 15 and then block interleaving isperformed by the block interleaver 124, and the case in which groupinterleaving is performed by the group interleaver 122 based on Equation16 and then block interleaving is performed by the block interleaver 124have an inverse relationship with each other.

In addition, the case in which group interleaving is performed by thegroup interleaver 122 based on Equation 17 and then block-rowinterleaving is performed by the block-row interleaver 125, and the casein which group interleaving is performed by the group interleaver 122based on Equation 18 and then block-row interleaving is performed by theblock-row interleaver 125 have an inverse relationship with each other.

Accordingly, the modulator 130 may map the bits output from theblock-row interleaver 125 onto a modulation symbol in the same method aswhen the block interleaver 124 is used.

The bit interleaving method suggested in the exemplary embodiments isperformed by the parity interleaver 121, the group interleaver 122, thegroup twist interleaver 123, and the block interleaver 124 as shown inFIG. 4 (the group twist interleaver 123 may be omitted according tocircumstances). However, this is merely an example and the bitinterleaving method is not limited to three modules or four modulesdescribed above.

For example, when the block interleaver is used and the groupinterleaving method expressed as in Equation 11 is used, regarding thebit groups X_(j)(0≤j<N_(group)) defined as in Equation 9 and Equation10, bits belonging to m number of bit groups, for example, {X_(π(i)),X_(π(α+i)), . . . , X_(π((m−1)×α+i))} (0≤i<α), may constitute a singlemodulation symbol.

Herein, α is the number of bit groups constituting the first part of theblock interleaver, and α=└N_(group)/m┘. In addition, m is the number ofcolumns of the block interleaver and may be equal to the number of bitsconstituting the modulation symbol or half of the number of bitsconstituting the modulation symbol.

Therefore, for example, regarding parity-interleaved bits u_(i),{u_(π(i)+j), u_(π(α+i)+j), . . . , u_(π((m−1)×α+i)+)} (0<i≤m, 0<j≤M) mayconstitute a single modulation symbol. As described above, there arevarious methods for constituting a single modulation symbol.

In addition, the bit interleaving method suggested in the exemplaryembodiments is performed by the parity interleaver 121, the groupinterleaver 122, the group twist interleaver 123, and the block-rowinterleaver 125 as shown in FIG. 14 (the group twist interleaver 123 maybe omitted according to circumstances). However, this is merely anexample and the bit interleaving method is not limited to three modulesor four modules described above.

For example, when the block-row interleaver is used and the groupinterleaving method expressed as in Equation 17 is used, regarding thebit groups X_(j)(0≤j<N_(group)) defined as in Equation 13 and Equation14, bits belonging to m number of bit groups, for example, {X_(π(m×i)),X_(π(m×i+1)), . . . , X_(π(m×i+(m−1)))} (0≤i<α), may constitute a singlemodulation symbol.

Herein, α is the number of bit groups constituting the first part of theblock interleaver, and α=└N_(group)/m┘. In addition, m is the number ofcolumns of the block interleaver and may be equal to the number of bitsconstituting the modulation symbol or half of the number of bitsconstituting the modulation symbol.

Therefore, for example, regarding parity-interleaved bits u_(i),{u_(π(m×i)+j), u_(π(m×i+1)+j), . . . , u_(π(m×i+(m−1))+j)} (0<i≤m,0<j≤M) may constitute a single modulation symbol. As described above,there are various methods for constituting a single modulation symbol.

The transmitting apparatus 100 may transmit the signal mapped onto theconstellation to a receiving apparatus 2700. For example, thetransmitting apparatus 100 may map the signal mapped onto theconstellation onto an Orthogonal Frequency Division Multiplexing (OFDM)frame using OFDM, and may transmit the signal to the receiving apparatus2700 through an allocated channel.

FIG. 18 is a block diagram to illustrate a configuration of a receivingapparatus according to an exemplary embodiment. Referring to FIG. 18 ,the receiving apparatus 2700 includes a demodulator 2710, a multiplexer2720, a deinterleaver 2730 and a decoder 2740.

The demodulator 2710 receives and demodulates a signal transmitted fromthe transmitting apparatus 100. Specifically, the demodulator 2710generates a value corresponding to an LDPC codeword by demodulating thereceived signal, and outputs the value to the multiplexer 2720. In thiscase, the demodulator 2710 may use a demodulation method correspondingto a modulation method used in the transmitting apparatus 100. To do so,the transmitting apparatus 100 may transmit information regarding themodulation method to the receiving apparatus 2700, or the transmittingapparatus 100 may perform modulation using a pre-defined modulationmethod between the transmitting apparatus 100 and the receivingapparatus 2700.

The value corresponding to the LDPC codeword may be expressed as achannel value for the received signal. There are various methods fordetermining the channel value, and for example, a method for determininga Log Likelihood Ratio (LLR) value may be the method for determining thechannel value.

The LLR value is a log value for a ratio of the probability that a bittransmitted from the transmitting apparatus 100 is 0 and the probabilitythat the bit is 1. In addition, the LLR value may be a bit value whichis determined by a hard decision, or may be a representative value whichis determined according to a section to which the probability that thebit transmitted from the transmitting apparatus 100 is 0 or 1 belongs.

The multiplexer 2720 multiplexes the output value of the demodulator2710 and outputs the value to the deinterleaver 2730.

Specifically, the multiplexer 2720 is an element corresponding to ademultiplexer (not shown) provided in the transmitting apparatus 100,and performs an operation corresponding to the demultiplexer (notshown). However, when the demultiplexer (not shown) is omitted from thetransmitting apparatus 100, the multiplexer 2720 may be omitted from thereceiving apparatus 2700.

That is, the multiplexer 2720 performs an inverse operation of theoperation of the demultiplexer (not shown), and performs cell-to-bitconversion with respect to the output value of the demodulator 2710 andoutputs the LLR value in the unit of bit.

In this case, when the demultiplexer (not shown) does not change theorder of the LDPC codeword bits, the multiplexer 2720 may output the LLRvalues serially in the unit of bit without changing the order of the LLRvalues corresponding to the bits of the cell. Alternatively, themultiplexer 2720 may rearrange the order of the LLR values correspondingto the bits of the cell to perform an inverse operation to thedemultiplexing operation of the demultiplexer (not shown) based on Table27.

The information regarding whether the demultiplexing operation isperformed or not may be provided by the transmitting apparatus 100, ormay be pre-defined between the transmitting apparatus 100 and thereceiving apparatus 2700.

The deinterleaver 2730 deinterleaves the output value of the multiplexer2720 and outputs the values to the decoder 2740.

Specifically, the deinterleaver 2730 is an element corresponding to theinterleaver 120 of the transmitting apparatus 100 and performs anoperation corresponding to the interleaver 120. That is, thedeinterleaver 2730 deinterleaves the LLR value by performing theinterleaving operation of the interleaver 120 inversely.

In this case, the deinterleaver 2730 may include elements as shown inFIG. 19 or 21 .

First, as shown in FIG. 19 , the deinterleaver 2730 may include a blockdeinterleaver 2731, a group twist deinterleaver 2732, a groupdeinterleaver 2733, and a parity deinterleaver 2734.

The block deinterleaver 2731 deinterleaves the output of the multiplexer2720 and outputs the value to the group twist deinterleaver 2732.

Specifically, the block deinterleaver 2731 is an element correspondingto the block interleaver 124 provided in the transmitting apparatus 100and performs the interleaving operation of the block interleaver 124inversely.

That is, the block deinterleaver 2731 may deinterleave by using at leastone row formed of a plurality of columns, that is, by writing the LLRvalue output from the multiplexer 2720 in each row in the row directionand reading each column of the plurality of rows in which the LLR valueis written in the column direction.

In this case, when the block interleaver 124 interleaves by dividing acolumn into two parts, the block deinterleaver 2731 may deinterleave bydividing a row into two parts.

In addition, when the block interleaver 124 performs writing and readingwith respect to a bit group which does not belong to the first part inthe row direction, the block deinterleaver 2731 may deinterleave bywriting and reading a value corresponding to the group which does notbelong to the first part in the row direction.

Hereinafter, the block deinterleaver 2731 will be explained withreference to FIG. 20 . However, this is merely an example and the blockdeinterleaver 2731 may be implemented in other methods.

An input LLR v_(i) (0≤i<N_(ldpc)) is written in a r_(i) row and a c_(i)column of the block deinterleaver 2431. Herein, c_(i)=(i mod N_(c)) and

${r_{i} = \left\lfloor \frac{i}{N_{c}} \right\rfloor},$

On the other hand, an output LLR q_(i)(0≤i<N_(c)×N_(r1)) is read from ac_(i) column and a r_(i) row of the first part of the blockdeinterleaver 2431. Herein,

${c_{i} = \left\lfloor \frac{i}{N_{r1}} \right\rfloor},$r_(i)=(i mod N_(r1)).

In addition, an output LLR q_(i)(N_(c)×N_(r1)≤i<N_(ldpc)) is read from ac_(i) column and a r_(i) row of the second part. Herein,

${c_{i} = \left\lfloor \frac{\left( {i - {N_{c} \times N_{r1}}} \right)}{N_{r2}} \right\rfloor},$r_(i)=N_(r1)+{(i−N_(c)×N_(r1)) mode N_(r2)}.

The group twist deinterleaver 2732 deinterleaves the output value of theblock deinterleaver 2731 and outputs the value to the groupdeinterleaver 2733.

Specifically, the group twist deinterleaver 2732 is an elementcorresponding to the group twist interleaver 123 provided in thetransmitting apparatus 100, and may perform the interleaving operationof the group twist interleaver 123 inversely.

That is, the group twist deinterleaver 2732 may rearrange the LLR valuesof the same group by changing the order of the LLR values existing inthe same group. When the group twist operation is not performed in thetransmitting apparatus 100, the group twist deinterleaver 2732 may beomitted.

The group deinterleaver 2733 (or the group-wise deinterleaver)deinterleaves the output value of the group twist deinterleaver 2732 andoutputs the value to the parity deinterleaver 2734.

Specifically, the group deinterleaver 2733 is an element correspondingto the group interleaver 122 provided in the transmitting apparatus 100and may perform the interleaving operation of the group interleaver 122inversely.

That is, the group deinterleaver 2733 may rearrange the order of theplurality of bit groups in bits group wise. In this case, the groupdeinterleaver 2733 may rearrange the order of the plurality of bitgroups in bits group wise by applying the interleaving method of Tables9 to 20 inversely according to a length of the LDPC codeword, amodulation method and a code rate.

The parity deinterleaver 2734 performs parity deinterleaving withrespect to the output value of the group deinterleaver 2733 and outputsthe value to the decoder 2740.

Specifically, the parity deinterleaver 2734 is an element correspondingto the parity interleaver 121 provided in the transmitting apparatus 100and may perform the interleaving operation of the parity interleaver 121inversely. That is, the parity deinterleaver 2734 may deinterleave theLLR values corresponding to the parity bits from among the LLR valuesoutput from the group deinterleaver 2733. In this case, the paritydeinterleaver 2734 may deinterleave the LLR values corresponding to theparity bits in an inverse method of the parity interleaving method ofEquation 8.

However, the parity deinterleaver 2734 may be omitted according to thedecoding method and implementation of the decoder 2740.

The deinterleaver 2730 may include a block-row deinterleaver 2735, agroup twist deinterleaver 2732, a group deinterleaver 2733 and a paritydeinterleaver 2734, as shown in FIG. 21 . In this case, the group twistdeinterleaver 2732 and the parity deinterleaver 2734 perform the samefunctions as in FIG. 19 , and thus, a redundant explanation is omitted.

The block-row deinterleaver 2735 deinterleaves the output value of themultiplexer 2720 and outputs the value to the group twist deinterleaver2732.

Specifically, the block-row deinterleaver 2735 is an elementcorresponding to the block-row interleaver 125 provided in thetransmitting apparatus 100 and may perform the interleaving operation ofthe block-row interleaver 125 inversely.

That is, the block-row deinterleaver 2735 may deinterleave by using atleast one column formed of a plurality of rows, that is, by writing theLLR values output from the multiplexer 2720 in each column in the columndirection and reading each row of the plurality of columns in which theLLR value is written in the column direction.

However, when the block-row interleaver 125 performs writing and readingwith respect to a bit group which does not belong to the first part inthe column direction, the block-row deinterleaver 2735 may deinterleaveby writing and reading a value corresponding to the bit group which doesnot belong to the first part in the column direction.

The group deinterleaver 2733 deinterleaves the output value of the grouptwist deinterleaver 2732 and outputs the value to the paritydeinterleaver 2734.

Specifically, the group deinterleaver 2733 is an element correspondingto the group interleaver 122 provided in the transmitting apparatus 100and may perform the interleaving operation of the group interleaver 122inversely.

That is, the group deinterleaver 2733 may rearrange the order of theplurality of bit groups in bit group wise. In this case, the groupdeinterleaver 2733 may rearrange the order of the plurality of bitgroups in bits group wise by applying the interleaving method of Tables29 to 40 inversely according to a length of the LDPC codeword, amodulation method and a code rate.

Although the deinterleaver 2730 of FIG. 18 includes three (3) or four(4) elements as shown in FIG. 19 or 21 , operations of the elements maybe performed by a single element. For example, when bits each of whichbelongs to each of bit groups X_(a), X_(b), X_(c), X_(d), X_(e), X_(f),X_(g), X_(h), X_(i), X_(j) constitute a single modulation symbol, thedeinterleaver 2730 may deinterleave these bits to locationscorresponding to their bit groups based on the received singlemodulation symbol.

For example, when the code rate is 6/15 and the modulation method is1024-QAM, the group deinterleaver 2733 may perform deinterleaving basedon Table 9.

In this case, bits each of which belongs to each of bit groups X₆₆, X₅₉,X₂₂, X₁₅, X₁₀₆, X₉₇, X₇₄, X₈₈, X₁₃₂, X₁₃₄ constitute a single modulationsymbol. Since one bit in each of the bit groups X₆₆, X₅₉, X₂₂, X₁₅,X₁₀₆, X₉₇, X₇₄, X₈₈, X₁₃₂, X₁₃₄ constitutes a single modulation symbol,the deinterleaver 2730 may map bits onto decoding initial valuescorresponding to the bit groups X₆₆, X₅₉, X₂₂, X₁₅, X₁₀₆, X₉₇, X₇₄, X₈₈,X₁₃₂, X₁₃₄ based on the received single modulation symbol.

The decoder 2740 may perform LDPC decoding by using the output value ofthe deinterleaver 2730. To achieve this, the decoder 2740 may include anLDPC decoder (not shown) to perform the LDPC decoding.

Specifically, the decoder 2740 is an element corresponding to theencoder 110 of the transmitting apparatus 100 and may correct an errorby performing the LDPC decoding by using the LLR value output from thedeinterleaver 2730.

For example, the decoder 2740 may perform the LDPC decoding in aniterative decoding method based on a sum-product algorithm. Thesum-product algorithm is one example of a message passing algorithm, andthe message passing algorithm refers to an algorithm which exchangesmessages (e.g., LLR value) through an edge on a bipartite graph,calculates an output message from messages input to variable nodes orcheck nodes, and updates.

The decoder 2740 may use a parity check matrix when performing the LDPCdecoding. In this case, an information word submatrix in the paritycheck matrix is defined as in Tables 4 to 20 according to a code rateand a length of the LDPC codeword, and a parity submatrix may have adual diagonal configuration.

In addition, information on the parity check matrix and information onthe code rate, etc. which are used in the LDPC decoding may bepre-stored in the receiving apparatus 2700 or may be provided by thetransmitting apparatus 100.

FIG. 22 is a flowchart to illustrate an interleaving method of atransmitting apparatus according to an exemplary embodiment.

First, an LDPC codeword is generated by LDPC encoding based on a paritycheck matrix (S3010). In this case, in the LDPC encoding, a parity checkmatrix in which an information word submatrix is defined by Tables 4 to8 and a parity submatrix has a dual diagonal configuration (that is, theparity check matrix of FIG. 2 ) may be used, or a parity check matrixwhich is row and column permutated from the parity check matrix of FIG.2 based on Equations 4 and 5 (that is, the configuration of FIG. 3 ) maybe used.

Thereafter, the LDPC codeword is interleaved (S3020).

Then, the interleaved LDPC codeword is mapped onto a modulation symbol(S3030). In this case, bits included in a predetermined number of bitgroups from among the plurality of bit groups of the LDPC codeword maybe mapped onto a predetermined bit of a modulation symbol.

In this case, each of the plurality of bit groups may be formed of Mnumber of bits, and M may be a common divisor of N_(ldpc) and K_(ldpc)and may be determined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Herein,Q_(ldpc) is a cyclic shift parameter value regarding columns in a columngroup of an information word submatrix of the parity check matrix,N_(ldpc) is a length of the LDPC codeword, and K_(ldpc) is a length ofinformation word bits of the LDPC codeword.

Operation S3020 may include interleaving parity bits of the LDPCcodeword, dividing the parity-interleaved LDPC codeword by the pluralityof bit groups and rearranging the order of the plurality of bit groupsin bits group wise, and interleaving the plurality of bit groups theorder of which has been rearranged.

Specifically, the order of the plurality of bit groups may be rearrangedin bits group wise based on the above-described Equation 15 presentedabove. In Equation 15, π(j) is determined based on at least one of alength of the LDPC codeword, a modulation method, and a code rate.

For example, when the LDPC codeword has a length of 64800, themodulation method is 1024-QAM, and the code rate is 6/15, π(j) may bedefined as in Table 9 presented above.

In another example, when the LDPC codeword has a length of 64800, themodulation method is 1024-QAM, and the code rate is 8/15, π(j) may bedefined as in Table 10 presented above.

In another example, when the LDPC codeword has a length of 64800, themodulation method is 1024-QAM, and the code rate is 12/15, π(j) may bedefined as in Table 13 presented above.

However, this is merely an example. π(j) may be defined as in Tables 11or 12 described above.

In addition, Equation 16 may be used in rearranging the order of theplurality of bit groups in bits group wise. In this case, π(j) may bedefined as in Tables 15 to 20 described above.

The plurality of bit groups the order of which has been rearranged maybe interleaved by writing the plurality of bit groups in each of theplurality of columns in the column direction in bit group wise, andreading each row of the plurality of columns in which the plurality ofbit groups are written in bits group wise in the row direction.

In this case, from among the plurality of bit groups, at least some bitgroup which can be written in each of the plurality of columns in bitsgroup wise is written in each of the plurality of columns serially, andthen, the other bit groups are divided and written in the other areaswhich remain in each of the plurality of columns after the at least somebit group has been written in bits group wise.

In operation S3020, the interleaving may be performed in other methodsin addition to the above-described method.

Specifically, the interleaving may be performed by using Equation 17 andTables 29 to 34 described above, or may be performed by using Equation18 and Tables 35 to 40 described above.

In these cases, the order of the plurality of bit groups may berearranged in bits group wise such that an arrangement unit, in which atleast one bit groups including bits to be mapped onto the samemodulation symbol is serially arranged in bits group units, is repeated.

When a plurality of bit groups are interleaved, the interleaving may beperformed by writing, in each row, at least one bit group including bitsto be mapped onto a same modulation symbol from among the plurality ofbit groups the order of which has been rearranged, in the row direction,and reading each column of the row in which the at least one bit groupis written in the column direction.

A non-transitory computer readable medium, which stores a program forperforming the interleaving methods according to various exemplaryembodiments in sequence, may be provided. The non-transitory computerreadable medium refers to a medium that stores data semi-permanentlyrather than storing data for a very short time, such as a register, acache, and a memory, and is readable by an apparatus. Specifically, theabove-described various applications or programs may be stored in anon-transitory computer readable medium such as a compact disc (CD), adigital versatile disk (DVD), a hard disk, a Blu-ray disk, a universalserial bus (USB), a memory card, and a read only memory (ROM), and maybe provided.

At least one of the components, elements or units represented by a blockas illustrated in FIGS. 1, 4, 13, 14, 18, 19 and 21 may be embodied asvarious numbers of hardware, software and/or firmware structures thatexecute respective functions described above, according to an exemplaryembodiment. For example, at least one of these components, elements orunits may use a direct circuit structure, such as a memory, processing,logic, a look-up table, etc. that may execute the respective functionsthrough controls of one or more microprocessors or other controlapparatuses. Also, at least one of these components, elements or unitsmay be specifically embodied by a module, a program, or a part of code,which contains one or more executable instructions for performingspecified logic functions. Also, at least one of these components,elements or units may further include a processor such as a centralprocessing unit (CPU) that performs the respective functions, amicroprocessor, or the like. Two or more of these components, elementsor units may be combined into one single component, element or unitwhich performs all operations or functions of the combined two or morecomponents, elements of units. Further, although a bus is notillustrated in the above block diagrams, communication between thecomponents, elements or units may be performed through the bus.Functional aspects of the above exemplary embodiments may be implementedin algorithms that execute on one or more processors. Furthermore, thecomponents, elements or units represented by a block or processing stepsmay employ any number of related art techniques for electronicsconfiguration, signal processing and/or control, data processing and thelike.

Although a bus is not illustrated in the block diagrams of thetransmitting apparatus and the receiving apparatus, communication may beperformed between each element of each apparatus via the bus. Inaddition, each apparatus may further include a processor such as aCentral Processing Unit (CPU) or a microprocessor to perform theabove-described various operations.

The foregoing exemplary embodiments and advantages are merely exemplaryand are not to be construed as limiting the present inventive concept.The exemplary embodiments can be readily applied to other types ofapparatuses. Also, the description of the exemplary embodiments isintended to be illustrative, and not to limit the scope of the inventiveconcept, and many alternatives, modifications, and variations will beapparent to those skilled in the art.

What is claimed is:
 1. A receiving method comprising: demodulating asignal received from a transmitting apparatus to generate values basedon 1024-quadrature amplitude modulation (QAM); splitting the values intoa plurality of groups; deinterleaving the plurality of groups based onan interleaving order; and decoding values of the deinterleavedplurality of groups based on a low density parity check (LDPC) code, acode rate of the LDPC code being 6/15 and a code length of the LDPC codebeing 64800, wherein the plurality of groups are deinterleaved based ona following equation:Y _(π(j)) =X _(j) for(0≤j<N _(group)), where X_(j) is a j-th group amongthe plurality of groups, Y_(j) is a j-th group among the deinterleavedplurality of groups, N_(group) is a number of the plurality of groups,and π(j) denotes the interleaving order, and wherein the π(j) isrepresented as follows: Code Rate Order of the deinterleaving 6/15 π(j)(0 ≤ j < 180) j 0 1 2 3 4 5 23 24 25 26 27 28 46 47 48 49 50 51 69 70 7172 73 74 92 93 94 95 96 97 115 116 117 118 119 120 138 139 140 141 142143 161 162 163 164 165 166 π(j) 66 21 51 55 54 24 56 2 43 64 58 67 2544 136 29 36 26 178 28 34 106 127 76 143 81 32 96 3 78 144 151 90 11 156100 141 129 146 122 73 112 104 134 82 95 133 164 Code Rate Order of thedeinterleaving 6/15 π(j) (0 ≤ j < 180) j 6 7 8 9 10 11 29 30 31 32 33 3452 53 54 55 56 57 75 76 77 78 79 80 98 99 100 101 102 103 121 122 123124 125 126 144 145 146 147 148 149 167 168 169 170 171 172 π(j) 33 1270 63 47 65 53 68 61 39 52 69 126 177 15 37 148 9 131 105 138 75 130 101107 86 98 16 162 150 175 83 155 159 128 88 132 125 174 169 168 79 154120 110 170 114 153 Code Rate Order of the deinterleaving 6/15 π(j) (0 ≤j < 180) j 12 13 14 15 16 17 35 36 37 38 39 40 58 59 60 61 62 63 81 8283 84 85 86 104 105 106 107 108 109 127 128 129 130 131 132 150 151 152153 154 155 173 174 175 176 177 178 π(j) 145 8 0 57 23 71 1 22 31 161 3830 13 45 46 152 50 49 167 117 173 113 108 92 111 158 172 139 74 142 8793 103 94 140 165 84 118 179 147 91 160 72 109 171 176 99 116 Code RateOrder of the deinterleaving 6/15 π(j) (0 ≤ j < 180) j 18 19 20 21 22 4142 43 44 45 64 65 66 67 68 87 88 89 90 91 110 111 112 113 114 133 134135 136 137 156 157 158 159 160 179 π(j) 59 14 40 42 62 19 17 18 4 41 2777 60 35 48 135 124 121 97 149 166 7 5 119 20 6 137 157 10 85 163 115 8980 102
 123.


2. The receiving method of claim 1, wherein each of the plurality ofgroups comprises 360 values.